Using the dou gomu that came in the beginner accessory set (it’s like half as long as in the picture) and I’m not sure how I’m supposed to use it. Am I supposed to peel the paper off of the bottom or keep it on? Which side rests on my leg and which one on the shamisen?
Here’s what I used to stick mine on 
Under the paper is an adhesive surface, which following the above instructions will let you attach properly.
Some types of dou gomu are laid on the lap, and some others have a sticky underside covered with a paper you need to peel off. Let me know what type of dou gomu you have. cheers!