For each group of Bugsnax presented to you, click one or more of your favorites from that group and press the "Pick" button. Eventually, your favorite Bugsnax will start appearing under "Found Favorites". You can continue as long as you like to construct an arbitrarily long list of your favorite Bugsnax.
In principle, this picker is perfectly accurate, provided you pick consistently - you'll correctly get your second favorite second, even if it's pitted against your absolute favorite early on, for instance. You can reorder your favorites after you've found them, but in principle you shouldn't need to.
Based off the Favorite Pokemon Picker, with the original code and instructions by antialiasis!