Washing dishes... a puddle of water follows the outline of the sink up on the countertop. It's a drop-down sink. Where is this water coming from?

"When washing dishes ". You either have a leak in the faucet or are splashing water onto the countertop.

Let water from faucet run for a few minutes without any activity. If you get a water line then faucet is leaking. If no water then you are splashing it there.

Cchuck

In the common pivot type kitchen faucets, it's most likely leaking through the rubber O-rings that seal the inner body of the spout barrel where it pivots. As much as I wish they'd come up with a better seal for that part of the faucet, O-rings are cheap and fairly easy to replace, but you should lube them with silicone grease, which is contained in most faucet O-ring kits.

If it's a Moen faucet, they will send free repair parts to the original owner under their lifetime warranty if its use is residential. They will also email you instructions on how to do it.

Any other brand will send such a kit too, and probably have instructions as well, but at a small cost.