Basin Lock Nut Leaking
You will need to shut off the main water supply going to the house, open a faucet or hose bib that is lower than the area you will cut the pipe. Before you cut the pipe pick up on new supply tubes and this type of new valve for under the sink. Replace both while you are at it. This is presuming the pipe coming in is 1/2"

Follow the instructions for installation!!!!

Get 2 new supply lines these are 30" you may not need ones that long. 

Hook em on up!!