My bathroom sink drips water. I tried to shut off the water underneath the sink. The cold water shut off but the hot water would not. It doesn't run as fast but I can't get it to shut off completely. In order to fix this what should I do?

Your angle valve washer is leaking needs to be replaced, Shut off water to the house, remove the packing nut remove the stem take it with you to a H/D or Lowe's get a new washer, replace and install then proceed with your repair, see the image below for more information, good luck.

John

John helped you to repair the hot water angle stop. Let me tell you what to shut off so you can repair the faucet.
There are several places to shut the hot water off.
1) Shut off the ncold water stop to the water heater.
2) you can shut the entire house down with the house shut off **OR**
Shut the water off at the meter or the pump and bleed the pressure down.
Do you need assistance repairing the faucet? Good luck, Tom