Go to the steam page and hit the request access button to join! Note that requests are approved in batches due to how the steam playtest feature works.
The playtest will be active up to release. Note that it it has a different selection of levels from the demo and is NOT balanced to be your first experience with the game.
The main purpose of the playtest is to offer players interested in the game a chance to give further feedback. This will help with balancing the newer levels. Playtesters will also get credited in the final game if they fill in the feedback form.
If you mainly want to get a quick idea of the game, the demo is ideal and unlike the playtest, it is available instantly and forever.
Lastly, if you get stuck in any level, I encourage you to post in the steam Forums as the difficulty needs some tuning.