This video describes how to replace the capicitors in an RV air conditioner.

CAUTION: Make sure to unplug your main power before working on the air conditioner.
Capacitors in alternating current (AC) circuits, like this air conditioner, don't store energy the way they do in DC circuits, but it doesn't hurt to be in the habit of discharging capacitors before working on them.
Capacitors in AC circuits are non polarized, meaning there are not positive or negative terminals, and the wires can be connected to either terminal.

My unit is a Coleman Mach, although other brands will be similar. When I turned on my air conditioner all it did was buzz so I took some steps to determine that the fan capacitor was not working. I identified the correct part, ordered a new one for $18.95 including shipping, and replaced it.
Here are the part numbers for the capacitors in my unit, although your unit might use different parts. Make sure that you order the same capacitors that came with your air conditioner.
Fan capacitor part # 14995461 7.5 MFD 370 volts
Run capacitor part # 14995721 40 MFD 370 volts
Start capacitor part # 14970871 88108 MFD

I ordered my part through Amazon from:
RV Wholesale Direct
41 Triangle Court
Carrollton, GA. 30116
They shipped the correct part quickly and for free.