The first step to fixing a double handle leaky faucet is to shut off the water supply to the faucet. This can usually be done under the sink by turning the water supply to the faucet off. If you're not sure how to do this, there should be a shut off valve somewhere under the sink. If your Delta faucet is leaking, you may not need to replace the entire unit. Instead, you may be able to fix it by replacing the cartridge. The cartridge is what moves the water in the faucet and controls the temperature and pressure of the water. If the cartridge is old and damaged, it can leak.