newbie with new Thor Four Winds Class C- questions?

What's the best way to determine if the battery is full? I'm not well versed on electrical stuff and know I need to learn it. I looked at the number on the inverter switch, which starts to beep in the mid 11's. When I'm charging with generator the number goes up to 13.7, but then once I turn off gen it goes down to about 12.7 .... but seems to start lowering pretty quickly. I'm wondering if this is from the "surface charge" that you mentioned.