Now that you have determined where the leak is coming from, it’s time to repair the problem.
If you determined the sink leak is coming from the water supply, you need to dry off all of the water supply lines and bottom of the faucet, then starting from the top run your hand down the lines and feel for water. Once you fell water, use a dry paper towel to pin point the leak.
If the leak is coming from the supply lines, it could be a hole in the line or a washer at one of the connections. Turn off the water and replace which ever part is bad.
If you find the leak is coming from the faucet itself, you will need to replace it.
See our article, http://www.homediyfixes.com/how-to-replace-your-kitchen-faucet/ for directions on replacing your faucet.
If you determined the issue is the kitchen sink strainer, Check out our http://www.homediyfixes.com/how-to-replace-your-kitchen-sink-strainer/ article and video.
If you believe it is in the actual drain piping, you may have a cracked pipe or bad gasket.
Most drains today are make of plastic and can crack or even loosen with the vibrations from using the sink. Sometimes they just need a little tightening or just replacing the gaskets in the joints.
Here is a great video with tips on finding a sink leak from Nick the Home Source Guy.