Hampton bay fan has white/black wires and green ground.
Electrical box has white/black/and red and copper ground.
What do I do with the red wire?
Even though switch is turned off at wall, when I connected black to black the fan comes on and stays on!
It does come with a remote.

Either leave it like it is and control only with the remote.. . Or if you want control from the wall switch as well, wire the fan's black to the red and cap off the house black.

For more information on ceiling fan wiring:

http://www.ceiling-fans-n-more.com/ceiling-fan-wiring.php