How does minecraft online work?

I'm getting minecraft for ps3 tomorrow, and I was just wondering if there's any open lobby's? From what I've read it seems like the only online you can do is with friends you have invited, or is their system different like you look up lobby's on the internet to find open ones (lobby's with random people joining)
Or will I just have to make new friends on minecraft to get invited to lots of games? Basically what I'm saying is, are there games with a bunch of random people as well as invite only lobby's, or is there only invite lobby's, it will be a problem for me because I have no one in my friends list who plays minecraft

Minecraft isn't for the PS3 It's only on PC and Xbox and you can play alone, invite your friends, or put in a code for a lobby but I think that's only for PC