Add up how much power (watts) you plan to use with your inverter, tv, dish etc. That info is usually on the product label. Divide that by 110. The result will give you amps (current). Batteries have an amp hour rating that determines their amount of amps available before recharging.
Example: Say you're using 1100 watts with your equipment and you run it for 1 hour; you would deplete your batteries by 10 amp hours, run it for 2 hours = 20 amp hours. So if your batteries were rated at 200 amp hours you could theoretically run your equipment for 20 hours before recharging your batteries. However, as a general rule discharging your batteries below 50% is not good and will reduce your battery life in most cases. So in the example I would not go beyond 10 hours without recharging the batteries.
Hope this helps you size the batteries you need. Also keep in mind that in addition to what you're running with your inverter other things in your RV will be drawing power from your batteries, like lights, water pump, fridge, etc. Some people use separate batteries for their inverter so they don't have to worry about that, however you will then need a charger for those batteries which some inverters have already built in.