After you have completed your placement matches you simply have to continue to play games. The result of your match, a win or loss, is what determines your rank. You will not rank up after a set number of wins and it will happen on its own.
The following restrictions are in place for matches from Rank D- to Rank A+:
You can rank up or down in matches:
- Solo queue
- A queue of 2 players
- A queue of 3 players
- A queue of 4 players
- A queue of 5 players