You are ranked separately in your 3v3 from your ranking in 1v1. What's more if you have a full team (which in 3v3 is a party of 3) then that ranking is separate from all others.
However, if you have a less than full team, your ranking will be 3s Random (which means 3v3 with at least 1 member being random), and is separate from any full team ranking.
For example you can have:
- 1s: Diamond 30
- 2 Random: Diamond 50
- 2s tzenes and McKay: Diamond 20
- 2s tzenes and BlueRaja: Gold 2
- 3 Random: Plat 10
- 3s tzenes, McKay, BlueRaja: Gold 20
All of these ranks are seperate, but if I play a 3s game with just McKay and I that contributes to my 3 Random ranking.
To start a match in 3v3 by yourself you would would select the 3v3 button on the multiplayer screen (here is an image I'll find a better one when I get home):