Put the mattress on a solid base if you want to firm it up. You can test this out by putting the mattress on the floor for a few nights. You could also put a board between a box-spring mattress and your firm mattress. If you want it less firm, put it on a box-spring mattress.
Put a duvet or memory foam over the mattress you currently have to soften it. Put a fitted sheet over it so the duvet or memory foam doesn't lose its place. You may need a new fitted sheet if the one you have is already snug. Memory foam can also reduce movement when you sleep, because it secures you it its grooves.
Flip your mattress over. Mattresses are meant to be rotated every couple months. This will help redistribute the components and give you a softer bed.
Stand your mattress up and hit it with a baseball bat. This is more severe than simply rotating it, but it will do a better job at distributing the materials.