When we set up the baby's room we got a changing pad and placed it on top of the dresser in her room instead of buying a whole separate changing table. It has a safety strap which we bolted to the back of the dresser so it doesn't fall off but it still slipped around a bit. My solution......drawer liner!
A roll of rubbery drawer/shelf liner
All you need to do is measure the top of your dresser and cut a piece of the shelf liner to fit the top. I did make it a bit smaller than the top so no edges peeked out from under the changing pad.
Then place your changing pad back on top. We also made sure to reattach it to the back of the dresser. Now the pad stays in place and doesn't slide around.