The Real-Time Ladder automatically creates games with players currently logged into the ladder. That's why you should leave the ladder when you leave WarLight and are not able to play, as otherwise the ladder may create a game, which you will be booted from. The good news is that if you get booted in the real-time ladder game, you will be automatically logged out of the ladder.
You will be proposed one game at a time. You cannot choose the person to play with it's random. Also, the map is random. You just log in to the ladder, play games, and then log out. It isn't possible to play with the same player more than once every 20 hours.