How it is SUPPOSED to work:
1.) You go through 5 placement matches to determine your rank.
2.) You get matched up with people on or about your "division". Say you get rank 25 in the silver division, it is supposed to match you up with players who have about you rank. In this case in the silver division.
3.) You do good to rank up higher.
The reason I say SUPPOSED is because one time I was bronze 45. It matched me up with a high gold person and a master.
Very rarely matches you with similar ranks, as it is very dependent on how many people are online in LP
No specific details with regards to how many points are awarded and such has ever been released. This is to prevent people abusing the system as much as possible... ie, attempting to stop people backing out of lobbies, or trying to keep the game close for more points.
As for which division you get placed in, well obviously the more wins you get the higher division you should end up in... ie, top 2% of players are in Masters, apparently. But the most people know about being promoted is that you need to go on a win streak, but there must be more to it as two people playing together don't get promoted together with the same win streak.
in short, any answers you get here will be a guess, an educated guess maybe, but still a guess as nothing has ever been detailed.