Switching to the battery is automatic. As soon as you unplug the shore power cable the battery will automatically kick in and power the lights, water pump, furnace, radio, etc.
The battery will not power any items normally powered by 120v AC. This includes all the outlets throughout the RV, the air conditioner, the microwave, coffee maker, toaster, etc. None of these will operate from the battery. You would have to add an inverter to the trailer if you wanted AC power from the battery. That's a whole other subject.
If your battery was at 12.25 volts immediately after you disconnected the shore power then your charger isn't working. However, the battery should, even at that voltage, allow the lights and pump to operate.
