I know I'm a little late to the party, but I did want to throw some interjections. (I would have commented but not enough reputation points yet, so, here's a full answer).
This requires the latest version of VS Code, Azure Repo Extention, and Git to be installed.
Anyone looking to use the new VS Code (or using the preview like myself), when you go to the Settings (Still File -> Preferences -> Settings or CTRL+, ) you'll be looking under User Settings -> Extensions -> Azure Repos.
Then under Tfvc: Location you can paste the location of the executable.
For 2017 it'll be
C:\Program Files (x86)\Microsoft Visual Studio\2017\Professional\Common7\IDE\CommonExtensions\Microsoft\TeamFoundation\Team Explorer\TF.exe
Or for 2019 (Preview)
C:\Program Files (x86)\Microsoft Visual Studio\2019\Preview\Common7\IDE\CommonExtensions\Microsoft\TeamFoundation\Team Explorer\TF.exe
After adding the location, I closed my VS Code (not sure if this was needed) and went my git repo to copy the git URL.
After that, went back into VS Code went to the Command Palette (View -> Command Palette or CTRL+Shift+P) typed Git: Clone pasted my repo:
Selected the location for the repo to be stored. Next was an error that popped up. I proceeded to follow this video which walked me through clicking on the Team button with the exclamation mark on the bottom of your VS Code Screen
Then chose the new method of authentication
Copy by using CTRL+C and then press enter. Your browser will launch a page where you'll enter the code you copied (CTRL+V).
Click Continue
Log in with your Microsoft Credentials and you should see a change on the bottom bar of VS Code.
Cheers!