I have a ceiling fan with black and a white wire that connects to the supplied voltage. The problem is that I have 4 wires (Red, white black and bare). Which wires do I connect to the remote? The output of the remote is Blue, Black, White and Ground.

Black to black (fan)
Red to blue (light)
White to white (neutral)
Bare to green (ground)
Be sure power is off.

Um, no.

You connect black to either black OR red (and cap off the other one), and white to white.

Ceiling fan wiring - Ceiling Fans N More

Reading again, don't know who's right. Are those 4 wires at ceiling? Or are those 4 from Receiver?

He has 4 ceiling wires, and a receiver that connects with two wires (to the ceiling). The receiver also connects with four wires to the fan.