K, I'm gonna give this a shot and see if I am doing this right- if I screw this up let me know.
Short answer- Add up number of watts you use in a day/week/whatever. That's the amount you USE/NEED
If your panels are 100 watts, figure out insolation (amount of sun) for your area- probably 4-7 hours average (panels only work well with very direct light early morning/late evening very little power) so most possible to get with that is 400-700 watts in a day. That's how much you MAKE
Batteries - Deep cycle- measured in Amp hours- so a 12 volt 10 amp hour battery holds 12 volts time 10 amps, or 120 watts.
Deep cycle batteries can be cycled up and down much more than car batteries, but if you empty them too much, they will die much faster.
Most good batteries will last 5 + years if you keep them above 50%.
So with 100 watt panel, (assuming 5 hours sun) you make 500 watts. Working backwards from above, 500 watts at 12 volts would fill a 40 amp hour battery in 1 sunny day, if all the power went into the battery. Since you never want you battery to drop below 50%, you would want 80 amp hours of batteries for that load.
That size system would provide 500 watts across a 24 hour period in absolutely perfect conditions (which never happens...you will have losses- rain, dirt on panels, loss in wires, loss inside batteries..... real world, maybe 70-75% of best is pretty darn good, so if you get 350 watts on 5 hours you are doing okay.)
