After two tries, I was able to get the leak underneath the dishwasher fixed. No more drip, drip, drip. We originally thought that the water supply line was not on tight enough and thought that was how it was leaking, but actually it was that gold connector piece that the water supply line is connected to that was actually leaking. That's 1/2 a point for me!
Underneath the dishwasher
So, the big problem is getting the white tube to connect to the air gap. This is what the white tube looks like - no connector piece at the end.
And this is what the one on my old dishwasher looked like.
That black piece is stuck on there pretty well - can't take it off.
And this is what they told me to buy at Home Depot.
Official name: "Disposal Connector"
I tightened up the clamp and then hooked it up to the air gap.
It was very hard to get back there because the garbage disposal is in front, so I crawled under there and tightened the top clamp as much as could. And oh boy, did it NOT work! Water came out everywhere. So, I figure that either I didn't tighten it very good or it's not the right part? I gave up for now - I have other things to do, but I'm determined to do this myself!