You didn't specify which device you own, but by the tag I assume it is a Nexus 5.
Flashing TWRP is pretty easy, especially on Nexus devices.
Download the newest .img file here:
Turn off your device. Turn on the device and keep holding volume down until a menu shows up. The device will now be in fastboot mode. Plug the device into your computer. If you have the right drivers installed, your screen should now say FASTBOOT USB. Run the following command via the command line (in the directory the ADB is installed):
fastboot flash recovery openrecovery-twrp-22.214.171.124-hammerhead.img
Note you will also need adb and fastboot for your computer.
If you don't have ADB or the correct drivers installed, I recommend downloading Wugfresh Nexus toolkit from here:
And follow the instructions for installing the drivers.
OR - if for some reason you're having trouble with the above, just download Wugfresh Nexus toolkit (link above) and select root my device (make sure to check 'install custom recovery').