Tub dripping

The tub faucet is dripping. The top two are for the shower as you can see. And I have the cold handle off. But what am to change in there?

You need (a) turn OFF the water supply, (b) remove the bonnets around the valve stem handles (they may unscrew or pry off, either one), and (c) unscrew the valves out counter-clockwise.
Take the valves to a hardware store and replace the rubber o-rings around the valves and the rubber washers on the ends of the stems.
Good Luck!
Mike

I dug away some silicone packed into the hole and removed another nut. But see here there is another nut recessed into the wall. Am I supposed to get this out too? How am I supposed I grab it? Thanks for the input.

And one other thing, water still drips from the tub spout even when the hot and cold are shut off.

faucet

Put the first nut back in so you do not damage the thread on the piece in the wall. Then unscrew the big "nut" that your included picture shows. The only parts you may find for that valve are washers and seats if they are removable, or one of the old American Standard Re-Nu units.