Testing new features mainly just involves interacting with it in every way imaginable, specifically those that users wont commonly do, that way you can quickly handle problems that are tougher to find if you solely interact normally with a site/app.

My best approach for testing is attempting un-intuitive actions that users normally wouldn't try, but are possible. These specific bugs are usually the hard ones to get picked up. Additionally, I think that it's best to harshly test things like search bars or filter types for any errors. Lastly, the most bare tests is testing every button and ensuring every output is as expected, even if reached from a different part of the app/site.