How should I wire a ceiling fan remote where two switches are used to control the fixture?
Start by turning off the power at the breaker, and verifying it's off with a non-contact voltage tester.
Connect all the bare or green grounding conductors together.
Connect the white wire from the ceiling to the white wire on the input side of the remote receiver module and the white wire in the fan.
Connect the black wire from the ceiling to the black wire on the input side of the remote receiver module.
Connect the blue wire from the output side of the remote receiver module to the blue wire in the fan.
Connect the red wire from the ceiling to the black wire in the fan.
Cap off the black and white wire from the output side of the remote receiver module.

Now when one switch is on, the remote will control the light. The other switch will turn the fan on and off. You'll end up with something like this.

Alternatively, you could wire it like this.

This way the remote module will control the fan (when the switch is in the ON position), and the other switch will control the light.
This answer assumes the black wire controls the fan, while the blue controls the light kit on the fan. Check the documentation that came with the fixture, for proper wiring instructions.