It would be nice to know what models furnace and water heater are in your trailer. The big question is whether they are spark ignition or if they require a pilot light.
On my 2005, the furnace will start automatically when the thermostat is raised (and gas is on). The same is true for the water heater in which I simply have to flip the switch on the wall and I will hear it spark and fire up. You just need to make sure that the water heater is full of water. The owners manual should cover how to use make sure the bypass is not set on the water heater. To be sure its full, you can flip the pressure relief valve on it for a second and water should come out.
If yours requires pilot lights you should see a big red dial when you open the access covers. It usually has you turn the dial to one setting, press a button and light the pilot and hold the button for 15-20 seconds after which the pilot is set and the items are ready to use.
Try searching Youtube for videos on camper water heaters or furnaces and you can probably find all kinds of useful info for manual or auto.