Overview
One user reported a method to do this on the CyanogenMod forums back in January, but it isn't exactly detailed.
Similarly, my path has three main steps, with varying levels of detail:
1. Install a custom recovery. I used TWRP.
2. Wipe the device.
3. Install CyanogenMod.
Root?
Note that I did not root the device. This is because I used Odin to install the custom recovery (TWRP). An alternative way would be to root the device and then install TWRP, without Odin; however, I shied away from rooting. There is more than one way to go about this.
Terminology
I do not explain certain concepts and terminology, but most are available here:

• http://wiki.cyanogenmod.org/w/Doc:_glossary
• http://wiki.cyanogenmod.org/w/Basic_concepts

Requirements

• One Samsung Galaxy Tab Pro 10.1 Wi-Fi
• A willingness to void your warranty
• A PC or Mac with admin rights for flashing the custom recovery
• A USB data connection cable An external SD card could be helpful

Furthermore, these instructions assume you have the stock Samsung ROM installed. If you've flashed before, probably you don't need this guide or can use it to figure out how to adapt it.
Step 0: Familiarize
If you are new to flashing, read through these instructions and some other resources (see below and search your own) to familiarize yourself before going ahead. In my case, I read for about a week before I decided to act.
Step 1: Play and charge
If your device is new, turn it on and play around with it. This way you can familiarize yourself with the stock ROM to see what you will not miss later once CyanogenMod is installed. Since I'm new to tablets and smartphones, I didn't hate TouchWiz, but the stock ROM did feel restrictive. Personally, I didn't even turn on Wi-Fi at this point, much less enter any account details or install apps.
Most importantly, charge the battery to at least 60%. I just went ahead and charged it all the way. If the battery were to die while you're flashing later, it would brick your device.
Step 2: Install a custom recovery
http://wiki.cyanogenmod.org/w/All_About_Recovery_Images
The custom recovery will allow you to install CyanogenMod. This is the most critical and the most involved step. I've divided it into several small steps and provided lots of detail in an attempt to anticipate questions and reduce confusion.
Note on the choice of custom recovery:
The CM wiki instructions suggest using ClockworkMod (CWM) or TeamWin Recovery Project (TWRP). From reading on the XDA forums, I gathered that TWRP is both easy to use—it uses touch buttons rather than using the volume and power buttons with CWM—and most importantly that it works well. Having used it, I can confirm that it not only works, it provides useful feedback and an intuitive interface. I haven't used CWM, but it is also known to work.
The following four steps (2.1 through 2.4) can be followed in any order.
2.1 Enable USB debugging
I assume your device is using the stock Samsung ROM. If so, select Settings, then General (top of screen) and select About Device (on the left, probably have to scroll down). Look for "Build number" and tap it seven times, and it will display "You are now a developer."
There is now a new menu entry "Developer options." Select it and then tick "USB debugging" and select OK when asked whether to allow. Now you can power off the device.
2.2 Install USB drivers on your computer
You need these to communicate with your device via USB cable. This guide provides instructions here for Windows 7. I understand that it also works on Mac OS X. (I don't use anything Apple.) GNU/Linux, though indicated in the CM wiki, is out of luck since Heimdall is known to not work (see the threads linked in the question).
There is a good guide for installing the drivers on Windows, the key parts of which are reproduced below. As an aside, Samsung Kies didn't work for me.
2.2.1 Download the Samsung USB drivers
The link from the android.gs guide
This provides SAMSUNG_USB_Driver_for_Mobile_Phones_v1.5.25.0-retail.exe You can get them directly from Samsung by entering your device, selecting Product Support and clicking on USB drivers, but companies like to change their web pages and drop support, so no guarantees. This provides SAMSUNG_USB_Driver_for_Mobile_Phones_v1.5.45.0.exe.
2.2.2 Scan the drivers with your anti-malware program (optional)
My scan gave no indication of a problem.
2.2.3 Install the driver package
Launch the exe file you just downloaded and provide the administrator password when prompted, follow the on-screen instructions.
2.2.4 Reboot
After completion of the install, reboot the machine. You'd probably never have guessed this one.
2.3 Install Odin
According to the instructions on the TWRP website there are two methods of installing TWRP that require you to root the tablet, which this guide avoids, and one that doesn't require root but does require Odin. A way with just FOSS would be better, but I did go this path, which is a weird one. Odin is leaked software, so there is no official download site. Fight a web site you can trust to obtain it; one possibility is another android.gs article. The version that worked for me is Odin 3.10.6. Odin 3.10.7 is also available, but not necessary.
If you mistrust using Odin, look at the instructions on the TWRP site, or use CWM.
2.3.1 Download Odin
Search for yourself, although there is a link in this guide (June 16, 2015). The link from that android.gs guide is this.
Wherever you download Odin from, be sure it's a safe download!
2.3.2 Extract archive and scan with anti-malware
The program is in a zip file, whose contents you can extract and scan with anti-malware.
2.4 Download the TWRP image
This is an easy one. Go here
Under Download Links, click "Primary (Recommended)" and then the most recent version with the .tar filename extension. Currently, this is twrp-2.8.7.0-picassowifi.img.tar (9 MB).
2.5 Install TWRP with Odin
All of the above steps should be completed before continuing with this step. Your tablet should be charged and turned off.
2.5.1 Launch Odin
On your PC, navigate to where you extracted (unzipped) the Odin files, and launch the executable. You don't need administrator rights. At least, I didn't.
2.5.2 Plug the USB cable into the PC
I had success with the white cable delivered with the device, but that may be different for you. It needs to be a data cable; some are only designed for charging. Do not plug the cable into the tablet yet.
2.5.3 Boot into download mode
The Galaxy Tab Pro 10.1 Wi-Fi has an unlocked bootloader, which is one reason we don't have to root it. It thus comes with a unique boot mode called download mode. To enter it, press these three buttons simultaneously for five to eight seconds:
Power + volume DOWN + Home
The first two are on the top edge, the Home button is the one in the middle on the front under the screen. See for example here.
WARNING!!! This is your last chance to not void your warranty. Samsung has a KNOX flag on this device, an e-Fuse that you very likely cannot reset. Continuing will void your warranty. Yes, Samsung has an unlocked bootloader and then voids your warranty if you use it. To me the tablet is only worth having if I can have control over it, so Samsung makes voiding the warranty a necessity.
2.5.4 Plug in the tablet
The USB should be plugged into the PC at this point, the tablet is in download mode, and Odin is waiting to see a device. Now plug the USB cable into the tablet, connecting it to the PC. This is the moment of truth whether the USB driver was correctly loaded. I had some doubt, because Windows popped up a dialogue with the spinning blue disc, saying "Searching Windows Update" for approximately longer than I could handle. It finally did work though, and the battery had charge.
You'll know it worked when Odin's "Log" window adds a text to show the detected device: <ID:0/003> Added!!
That's what it read for me, anyway. Where Odin says ID:COM above several bars, there will also be a light blue background with the first tab listing 0:[COM3].
2.5.5 Set up Odin for flashing
Click on the Options tab to the right of Log, and make sure only the following two entries are checked:

• Auto Reboot
• F. Reset Time

The others should NOT be checked. Checking/ticking the wrong boxes here could brick your device. See here for some explanations of Odin terminology.
Now check/tick on the box next to the AP button. In earlier versions of Odin this button is apparently the same as the PDA button. Against my expectations, the BL (bootloader) button is not correct; the twrp.me instructions explicitly mention to use the PDA button (now AP). Browse to the TWRP .tar file you downloaded in step 2.4 and select it. Do not press Start yet.
2.5.6 Double-check everything
Seriously, do.
2.5.7 WAIT: Read this before pressing Start
We are about to flash TWRP to the device. The flashing goes very fast on this device, only a few seconds, and then the boot happens right away. The stock ROM will probably overwrite TWRP if allowed to boot. To prevent this, you want to boot immediately into recovery mode as described below. You need to have the tablet in your hands and be ready to press the keys as soon as you see it is rebooting.
2.5.8 Press Start and enter recovery mode
After pressing start, the tablet will soon reboot. To enter recovery mode, press and hold the following two buttons simultaneously:
Power + volume UP
If it worked, you will be greeted with the blue (in version 2.8.7 at least) TWRP splash screen.
If you missed entering recovery mode (I did the first time), Samsung will start your tablet as usual. Don't panic. Power down the device and repeat the preceding steps, starting with 2.5.2.
The next time you boot into download mode, you may notice the following line:
KNOX WARRANTY VOID: 1
Be glad that you are now out from under Samsung's oppression. :)
Congratulations. The rest is pretty painless, even fun!
Step 3 Use TWRP to install CyanogenMod
TWRP is powerful software. Respect it, but don't be afraid. It's actually easy and fast.
3.1 Pick your CyanogenMod
Based on the 36-page thread on CyanogenMod 12.0 Nightlies for the Tab Pro 10.1 Wifi (picassowifi) (link), the June snapshot is stable for daily use, and that is my experience so far. (The 12.0 nightlies were discontinued sometime in April with the advent of 12.1 nightlies.) If that's the version you'd like, get the snapshot here
The CM12 June snapshot filename is cm-12-20150626-SNAPSHOT-YNG4NAO0A0-picassowifi.zip(231.71 MB)
Do not unzip the file. I recommend transferring it to the SD card in its own folder.
Note on file integrity:
Note there is a sha1 sum listed below the download. You can use this to check the integrity of the downloaded file. If you can use the PC to transfer this file to the Android storage, you can use the PC to check the file integrity after download (easy on GNU/Linux and probably on Mac, may need to download a utility on Windows). In my case, I couldn't get the PC to see the Android storage, so I ended up turning on Wi-Fi to download the CM12 snapshot directly on the device. If you want, "there's an app for that."
3.2 Back up (optional)
Restart the tablet in recovery mode (see 2.5.8 above), so that you are TWRP. If you want, you can back up the stock ROM to revert to in case of eventual trouble. I recommend putting this on the external SD card.
3.2.1 Press Backup
3.2.2 Set backup name (optional)
If desired, give a meaningful name; note it includes the date and build number, mine was KOT49H.Tt520XXUAOB1. I also clicked to enable compression (smaller file size, but takes longer) and allowed MD5 generation (for an integrity check when restoring, I believe). Use the enter key when done. (Took me a while to get this.)
3.2.3 Select Boot, Data and System
3.2.4 Swipe to Back Up
When done, return to the home menu
3.3 Wipe the tablet
This is a crucial step for correct flashing.
3.3.1 Press Wipe
3.3.2 Press Advanced Wipe
3.3.3 Make selections
You want these four:

• Dalvik Cache
• Cache
• Data
• System

Do not select Internal Storage or external_sd.
3.3.4 Swipe to Wipe
This will go fast. When done, return to the home screen.
3.4 Install CyanogenMod
Go for it!
3.4.1 Press Install
3.4.2 Select the CM zip you prepared
You can use the Folders area on the left to navigate between external (SD card) and internal storage, wherever you stored the zip file in step 3.1. Select the file, making sure it's the right one. You can select "Zip file signature verification?," which I suspect also verifies the file integrity.
3.4.3 Swipe to Confirm Flash
Shouldn't take long, actually.
3.4.4 Return to Home menu
When done!
3.4.5 Press Reboot
3.4.6 Press System
3.5 Boot into CyanogenMod
You should now see the CM logo animation and walk through the device setup. Rejoice!
Notes
Note on GAPPS:
I want to get away from Google and did not install the standard Google apps. If you want to do that, it's your homework.
Note on Google leftovers:
Unfortunately, CyanogenMod is not entirely free or open-source software—there are remnant proprietary Google components. You theoretically can remove these using a script called freecyngn. Sadly, I haven't been able to confirm yet that it worked on my device.
http://forum.xda-developers.com/showthread.php?t=2550769
NB: I didn't know how to take screenshots, but experienced helpers are welcome to do add images.

Url to this pages:
http://nade.dk/web/nade/site.nsf/FramesetHP?readform&wmain=files/Install_Cyangenmod_On_Samsung_Galaxy_Tab_Pro_10.1