They would be the stops under the sink for each of the cold and hot waters
If this faucet has a spray hose, turn on the faucet and open the spray hose.This will adjust the diverter in the kitchen faucet to the spray and pressureize the hose.This will allow the faucet to equilize and the sputter will stop if the spray diverter is working. It could be that the diverter part in the faucet is defective.
You take it apart and change the seals and washers.
Often a faucet will sputter if there is air in the lines. This happens if the water has been turned off and then on again. If this is the cause, it is only necessary to run the water a while and the air will get out of the lines, and the sputtering will stop.
replace or tighten the seals in the faucet.
Either replace the washer on the hot side in the faucet (or buy a new washerless faucet), replace the "angle-stop" with a "quarter-turn" style, or install a "water hammer arrestor". (There is a real convenient style on the market, it fits between the incoming nut at the angle stop and the thread on the body of the stop itself).
The system may need a rebuild. depending on the brand, the faucet can have the internal ball and gaskets replaced to stop the leak.
I just installed an American Standard kitchen faucet and it continues to run for a second or two after turning the handle. I called AS and they said it is because of the high arch and the location of the stop valve lower in the fixture. I think it may have more to do with this being a lower end kitchen faucet. During a bathroom remodel we installed a high arch Pegasus bathroom faucet and, while it is admittedly not at high as the kitchen faucet, it stop immediately and doesn't continue to run/drop at all. When I removed the Pegasus faucet filter at the spout, it behaves just like the kitchen faucet, so there's some sort of stop valve element at the spout of the Pegasus that isn't part of the AS faucet.
The rubber stop washer has failed.
I need to perform a faucet repair. How do I stop a leak that is caused by the screw not being tight enough on the valve?
Most likely, air in the line.
You take the faucet apart and replace the washer and stem seal .
Someone may have shut off the water to that faucet, or a pipe may have froze, or there may be air in the pipe.