You need a new cartridge. If it is a Moen it is guaranteed for life. Call Moen or take the old cartridge to any moen dealer. They will hand you new one free.
You need to identify exactly whose faucet you have. Solutions vary from company to company. As stated before, some have cartridges, some have rubber grommets and springs, etc...My sink has a single handle which controls water flow by lifting up/down or moving left/right. However, recently, whenever I bring it back down, the water won't turn off. Sometimes, I have to turn left or right to hit the perfect spot to turn off. Does anyone know what the problem is and how to fix this? Thanks for the assistance.