A Delta has a ball valve under the dome under the handle that operates over a hot and cold set of two rubber-tip seats on springs. The seats and springs are usually what wear out and have to be replaced from time to time.
You may be able to stop the drip for a time without having to replace the seats and springs yet by adjusting the pressure of the ball onto the seats.
You don't have to turn the water off for this adjustment.
Remove the handle with an Allen wrench-that-fits to loosen the recessed set screw and pull the handle up off of the stem of the ball.
There will be a plastic ring with either two or four small notches in it around the inside of the dome cap. Stick the ends of pair of needle-nose pliers into two opposite notches and turn the plastic adjusting ring clockwise with the water turned on. When it stops leaking (hopefully), you should be OK for a while. If it doesn't stop leaking, then you will have to replace the seats and springs, which are readily available at most any plumbing supply, hardware store or big box.
It's easy, and we can tell you how when you need to.