A drip under the sink is almost always a loose P-trap connection or a worn slip joint washer. Both are simple fixes that require no special skills.
Dry everything under the sink. Run water and watch carefully to see exactly where the drip is coming from. Use pliers to tighten the slip nuts at both ends of the P-trap. Run water and check.
If tightening doesn't stop the leak, the slip joint washers are worn. Loosen the slip nuts, remove the P-trap, and inspect the washers inside each nut. Replace any that are hard, cracked, or deformed. Reassemble and test.
If the leak is at the drain basket, the putty seal underneath has failed. Remove the drain basket, clean off old putty, roll a fresh rope of plumber's putty and press it under the flange, and reinstall.