I am installing 3 recessed lights. When I removed the old fixture I was surprised to see 4 sets of wires. One went to the light switch, another went to the power supply, and the other two went to various other rooms in my house. Can anyone look at my diagram and tell me how to hook up the three lights?

Connect F, A, and C together with all of the lights whites.
Black E, B, and D will connect to the switches white, which shold have black tape at both ends to reidentify as a hot.
Then Black from the switch to the lights blacks.
Connect all ground together.

Thank you so much. Your information has made this very easy to understand. I have done exactly as you described. I have one small problem though. The center light is on when the switch is off and the other 2 lights are off when the switch is off and when I turn the switch on the center light goes out and the other 2 lights come on.

You have a couple of lights in series, recheck your light connections, the black from the switch, connects to all lights blacks.
All whites connect together with Lights in and out to power/recepticles.
The white that goes to the switch will not connect to these whites.

I took everything apart and put it back together and it works now. Thank you again. The only thing I did differently was I used the black wire from the switch as the hot wire instead of using the white wire as you suggested. I don't know if that mattered at all but I am happy it is working. All I have to do now is repair the hole I left in the ceiling.

Electrically it doesn't matter, code does. I believe it is safer to have a white wire as continuously hot, as opposed to being switched, Less likely of a surprise, Black you assume hot.
You should have had wrapped black tape around the white wire from the switch at both ends. It will work if you don't, just Not code and a little more dangerous.
Glad you got it.