I haven't been on this site for too long myself, but lemme try to break down what I know as best I can:
You can change your layout by going to the "Layouts" section at the top of the screen. Choose a layout you like from the list, copy the code, comment "using" in the comment section as is SpaceHey tradition, and paste the code into your "about me" page on your profile. The code itself won't be visible on your profile page, but it will be customized. If you're already familiar with image files and YouTube links, you can go back into the code and switch out a few things to your liking. You can also copy-paste multiple layouts as long as they don't conflict, like having a spinning profile picture, a nice background, background music, the works.
Groups are, well, groups of people who want to discuss specific topics that the forums don't already cover or are too broad for (like a specific aesthetic, or a video game, or a tv show). You can think of these as "subreddits" in how similar a purpose they serve. Groups have their own forum and bulletin board (a type of temporary post that expires within a maximum of 10 days) to discuss the topic.
As for friends, you can send in a friend request if you like someone's profile layout, if you have a common interest, basically just about any other reason you'd make a friend request on an online game you like. Although, SpaceHey is a pretty small website with close to 3 million users and only 40k to 50k active users. It also has an outdated notification system, as the website doesn't go into your device's system to notify you if someone texts you or your forum post gets comments. I'm pretty guilty of forgetting that this website exists because of this. But don't let this discourage you from going out and trying to make friends on this site. Post about things you like on your blog, a forum, or a group of your choosing and your would-be-friends will find you. Just be aware of the bumps on the road, y'know?
I hope I covered everything in a succinct way that doesn't feel like I just threw the book at you. Go out there and have fun.