How do I connect a hopper and dropper so my dropper will drop something when I put an item in the hopper?

You're probably going to want to hook up a pulse circuit to both (by placing a sticky piston in the ground, placing a redstone block on top, and then placing a piece of redstone on the ground next to the sticky piston, or (this is a separate solution) you can use a comparator next to the hopper, and then hook a repeater up, and attach the redstone lines to both.

How about you put your hopper on the dropper, place a comparator facing the hopper, and wire up the comparator to the dropper? If that doesn't work, then follow this blueprint:
151 111 21 34 The 1 is redstone dust, the 2 is the comparator facing 3, which is a hopper pointed to 4, a dropper. And finally, 5 is a repeater facing right. This is a bird's eye view. Hope it works!

Use the picture below and put a hopper on top of the dropper