Each floor contains a few objects that need your help. In order to help them, simply tap on them and create the shape they request with your Sticks & Rings on the mat.
There are 3 floors in Shape Builder, and each floor has different objects you can interact with. Some objects will require you to complete certain tasks before you are able to move on to the next floor.
You will start on the first floor, with the Oven. If you feed the Oven enough, you'll unlock floor 2, which has the Easel. If you paint enough portraits on the Easel, you'll unlock floor 3, which has the Theater. You can use the Elevator to travel between floors.