You should have 2 valves under the sink you can shut off.
After removing the handle and unscrewing the stem...
stem
Still inside the faucet body there is a seat. Note on some of the cheaper brands they are not removable. The seat unscrews with a special wrench set using the right one to fit it... It is best to replace them but smothing them with sandpaper works well in a pinch. The water leaking past the washer erodes the seat and if the seat is not replaced or, resurfaced it will be rough and ruin the new washer when you install it. The seat if replaced must be a perfect match or it may ruin the faucet.
seat **********************************seat wrench set
