Start by bypassing your hot water heater. Then drain tanks, valves and any other place that water can be trapped. Then use a blow out plug to blow air through the lines and get them as empty as possible. Then, if you want to be absolutely sure you've got all the water out, pump antifreeze through the system to guarantee you haven't left any water in hard-to-remove places like toilet valves or plumping traps.
If you use the right tools and take care not to forget any of the hidden spots, you'll quickly and easily prepare your trailer for freezing weather.