I'll add to what Duff offered, but I'll offer this with a caveat: this is only based on my experience, and I consider myself far from seasoned when it comes to poker play in casinos.
First, it depends on the particular poker room and the particular day. Said differently, some poker rooms have different games going on, and they can be different depending on the day. However, usually, poker rooms normally have a number of cash games going on at any particular time. And, usually, they have some pot limit games and some no limit cash games going on. Further, those games usually have buy-in limits, but no table limit. That means that you can't go buy $10k in chips and then sit down and immediately start bullying everyone. Rather, they will cap the buy in per table, like $200 or $500 or something like that. However, there's no limit to the amount of money you can make when you're at the table. So, if someone does well and amasses $10k just sitting there for a few hours and taking everyone's money, then that entire $10k is in play - they can use it to bully other players (kind of like what happened in Duff's situation).
Some poker rooms will have tournaments that are played at certain times (like weekends). There it's just like it normally is: you pay X amount of money to get in the tournament and they pay out the top X amount of spots.
Almost everytime I've gone to a poker room, my experience has been the same as Duff's, wherein you have to check in and put your name on a list for the game you want to play and then wait for either a spot to open up at the table or enough guys that sign up so that a new table can be started.
Unless it's a tournament, there are no rules about when you can get up and leave. I've seen guys sit down at a cash game, win a big pot on their first hand, and then immediately get up and walk out. The other guys at the table kind of whined about it - calling it "poor form" for someone to just sit down and take everyone's money and then immediately leave without giving the the "chance to win it back" - but, the way I see it, that's the way it is. If you don't want a guy walking away with your money, don't lose it to him.