This answer assumes you're playing on PC or Mac, since the PTS isn't available for Xbox or Playstation.
On the ESO launcher screen, before you actually launch the game by clicking the "Play" button, there should be a little gear icon up in the corner. Click that icon and you should get some "Settings - Launcher." One of those settings should be a checkbox that says "Show Public Test Environment." Click on that to put a check in the box, then click "Apply" down below.
As already mentioned, the PTS is a second installation of the game, so you'll need to have enough free space on your system, and the initial installation might take a while.
Once the PTS has been installed, the launcher should list two things under the "Games" category-- "The Elder Scrolls Online" and "The Elder Scrolls Online (PTS)." Click on whichever one you want to launch, then click the "Play" button to launch it.
Thank you all, I found the PTS under games (it was greyed out a bit) and will give it a try once I clear up some disk space.
Whichever of the two versions (live or PTS) you click on will be in bright white text to indicate that it's currently selected, and the other version will be in dimmer text to indicate that it isn't selected.
Thank you for your question regarding the PTS. With the OP question now answered, we are going to close the thread. Our FAQ below explains how to get access to the ESO PTS.