Thanks for the speedy responses. I think I'm making some progress
here.

The wiring is in place for a three way switch. Only a single pole
switch was installed however.
I have 3 wires coming into the switch box. Each has a black and a white
and a ground.

There are 2 lights (A) and (B) in the room. Only one switch currently
operates light (A) and the other switch operates light (B). I want to
keep it this way. One switch each.

Light (B) though has the wiring for a 3 way. But, only a single pole
switch. This is where I want to put the dimmer. I tried just connecting
the 2 leads (Both black) from the dimmer to the 2 blacks that operate
the single pole switch. No good.

The single pole switch had a black wire connected to the sigle black
and a black connected to the 2 joined black wires.

I'm thinking only one of the black wires is hot. Because when I
uncouple the 2 that are together, light (A) goes off.

I really hope this isn't as confusing as I am confused.