Fix the part of the single-handle faucet that causes the issues. For example, if the spray head is leaking, replace the assembly containing the spray hose. If the spray hose won't send out water or somehow fails to divert the water, replace the diverter assembly or clean the existing one.
If the faucet leaks from beneath the handle, replace the ball assembly. Make sure that you purchase the part matching the type of handle, whether it's a lever or knob. The cam and packing beneath the handle usually also needs replacement in the case of a leak. Refer to the manufacturer's specifications when choosing the replacement parts specific to your faucet.
If the single-handle faucet leaks from the base of the spout, replace the O-rings, which keep water from leaking through that gap. If the aerator has leaks, replace the springs and seats, and turn the faucet back on. If the leak remains, the ball assembly for the faucet needs replaced.
Home improvement centers and plumbing supply stores sell replacement parts for faucets. Contact the manufacturer's customer service line for help with troubleshooting your particular faucet as well as for help finding a local retailer that carries the parts you need.