I am installing a multi-speed ceiling fan with lights. The ceiling box has a red wire for the lights. Do I connect both the black and red wire from the box to the black wire from the fan? Thanks!:D

First are you controlling the light separately from the fan at the wall with a light and fan switch independent of each other or a pull chain at the fan. Or does the fan have a remote control because it makes a difference on how it gets hooked up.. \
If you are having the fan and light independent of each other at the wall switch you will need 3 wires at the ceiling usually black, red, white, not including the ground wire usually green. If you only have 2 wires in the ceiling white and black you can't operate the fan and light separate of each other unless there is a remote control then its possible. So the red would probably go with the black and then you would be using the fan with the pull chain.
Black from fan and Red from fan light to Black in ceiling
White from fan to white in ceiling
Green to junction box and you would then be set...
Bill

I take it it is a remote fan?

You connect the fan to red and white OR black and white, not both.

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