Level the trailer and hook up water and power. Fire up the water heater after you purge the air from the lines. hopefully the PO left some propane in the tanks. Fire up the fridge on electric and monitor that it starts to get cold. Once it starts to get cool switch to propane and make sure it continues to get colder. The list goes on, but in general test all systems (heater, stove, microwave, shower, toilet, sinks, lights, 115 outlets, converter, batteries) Haul your shop vac into the trailer and start vacuuming all the carpets and cabinets. While doing this look for signs of water damage or outright leaks. Give her a good cleaning and you'll find things that need attention. In other words fire it up in the front yard and use it. We had a water leak after we bought our trailer used and found other minor problems. I'm sure there is more and others will chime in to help. Make a repair list then start camping!
Dave & MJ
1988 32' Excella 1000 (Beauty)
1999 White Dodge SLT Laramie 3500 Dually, 4x4, 5spd, 5.9 CTD 265k+ (The Beast)