If you sit on the toilet seat and it moves around, your need to tighten the bolts for the toilet seat hinges that hold the seat to the toilet.
Close the lid and you will see hinges on the back of the seat. You won't see any screws because they are under the flat caps that cover the hinges. These pop up with the help of a screw driver.
THEY POP UP FRONT TO BACK. In other words, the hinges for these caps are on the back, away from the seat. Inside you will see a screw head. The bolt is generally plastic and your will need a slotted or phillips head screwdriver.
Kneel in front of the toilet facing the back and reach underneath. You will feel the long bolt going through the toilet. Reach up until your fingers touch the plastic nut underneath. This usually has a flange that rests against the porcelain. Take a large blade screwdriver, either slotted or phillips, insert in the screw head. Push down on the screwdriver and tighten SLOWLY BUT FIRMLY. Keep your other hand on the nut to make sure it doesn't rotate as you tighten. Once both are tightened, make sure the seat doesn't move. If the toilet seat moves, try to tighten again. If it doesn't move, tighten to your satisfaction.
Also, you may want to replace the seat if it worn or the paint is coming off. Worn areas are harder to keep clean and tend to be an area where germs collect, on the under side where you can't see!