STEP 1: turn off the water valves under the sink.
STEP 2: remove the existing hardware. This part could have been easier, but I was unable to disconnect the final nut securing the faucet to the countertop. Here is a picture from underneath the sink looking up at the underside of the cabinet:
While I was trying to loosen the nut, shards of metal were dropping down on my face. I decided to put on protective goggles, and went into the bathroom to flush my eye with water. Still unable to get this nut loose with my adjustable wrench, I decided to go to Lowes to purchase a plumbers wrench which did the trick... albeit a little challenging.
STEP 3: Insert new hardware
I purchased a new gasket to act as a washer between the faucet and the countertop. Not sure if this was the correct product, but it seems to work well so far and the old one completely disintegrated.
I also had to insert a spacer underneath the countertop for the faucet to sit plumb and needed to remove the old copper tubing completely and connect the hot and cold tubes to the water valves. Using plumbers tape helped and a lucky guess led me to securing hot to hot and cold to cold on the first try.
STEP 4: Test
Success!
Total work time: 75 minutes (not including trip to Lowes). Difficulty level: 3 out of five.