I don't even know where to go to catch and/or acquire pets...

Have you followed the tutorial? There should be a box in the lower right corner of your screen. Follow those prompts and links. You can't catch a pet right away, but eventually you'll get the "capture a sylesti" quest, where you capture a pet for the first time.

But before you capture a pet, you get to create your first one! Honestly, I don't remember exactly which prompt I followed to create my first pet, but I used a generator to do it. Basically, follow all prompts you are given until the tutorials end; that'll get you everything you need. The site's a little confusing to navigate at first, but you get used to it pretty quickly. Maybe someone else who actually remembers the early stages of the tutorial will be able to chime in and give you more specific instructions. Welcome, and let me know if there's any other way I can help out!