As expected, Android devs are at it yet again. Nifty developers at Teamwin have released their TWRP recovery for the new Nexus 7 tablet (codename Flo). As always flashing the custom recovery on Nexus devices is easier, all you need is a bootloader unlocked new Nexus 7 and you are in business.
You will need ADB and Fastboot files at your end to finish all these tasks. You can simply install the latest version of Android SDK or you can get the relevant files (a simple Google search for ADB and Fastboot files for Nexus 7 will do the trick).
Detailed instructions to flash TWRP on the new Nexus 7 and achieve root are available at this XDA thread, which is also the best place to find support in case you mess something up.
If you have already rooted your Nexus 7 (2013) using something method, flashing TWRP is even easier, use the Goomanager app from Google Play to directly flash the recovery without any mess.