Depending on what type of pump you have it may have a quick connect type fitting like mine. I just disconnect the line and let the water drain out. I will also burp the pump a couple times while blowing the lines. I connect my air line to the fresh water hook up so when you run the pump it will let air blow through it.
I have gravity drains on both hot and cold that will get most of the water out of the system, I open those valves and then all the faucets. I also pull the plug on the water heater and drain it. After everything drains I'll close all the valves, hook up the air and then go through and open each faucet individually and keep rotating until no more water is blown out. Also remember to drain the Washer/Dryer, mine has a drain and the lint screen. Also flush the toilet several times to get water out of those lines and also the ice maker line. I also make sure the ice maker water solenoid valve is clear of water. I'll then pour RV antifreeze down the Pee traps.
I've used this general method on 2 RV's over 19 years and never had a problem.
2002 Monaco Windsor 38 PKD
2005 Jeep Grand Cherokee w/5.7 Hemi