You may have a couple of problems. First, it appears your stop valves are not working. This can be from calcium build up clogging the valves or lack of use. (They should be lubricated with oil or WD40 and turned every 6 months.)
To fix that required either a plumber or the proper tools. You need to shut off the water at the main line and drain the pipes to below the level you are working at. Then you need a valve puller. If you have enough pipe sticking out the wall you can cut the valve off. Most plumbers use compression 1/4 turn angle stop valves. Avoid the gate valves, they alwasy see to go out fast.
Once the stop valve is replace you can deal with the faucet. You can either take the faucet apart and clean it or relplace any gaskets, depending on the type. Or just replace the whole faucet. I usually go this route as by the time the gaskets go out the faucet has seen better days.
So why spend 50 cents when you can spend 50 bucks!
This isn't hard to do, but you do need to right tools to do it right and without frustration.