How to wire my ceiling fan remote with top and bottom lights
First, you closely examine the junction box to determine if the box is fan-rated.  If it is not fan-rated, the weight and vibration will tear it out of the ceiling, and you'll have a heavy, spinning fan drop in a guest/kid/mother in law. 

Second, all the grounds go together.  Grounds are green, green/yellow, or bare.  Do ground first, always. 

Next, all the neutrals go together.   Neutrals are white or gray in this installation.

Next, you connect the fan control module to the fan as instructed by the instructions.  We can't give you further guidance here; the instructions to the controller and fan tell you what to do. 

At this point you will have a black wire left from the fan controller.  You will also have a black wire left from the ceiling.  These go together.