It depends on your seniority, timing and the airline.
1. When you are hired at any airline you will be on reserve. How much you fly depends on how much flying is available at your airline for reserve pilots and the reserve system itself. Most airlines have a seniority based reserve system. If you are senior and on reserve, you can choose to fly or not fly. My airline (ASA), has a graft and corruption reserve system. How much/little you fly depends on your willingness to give shedulers kickbacks and bribes. Sounds as if I am kidding, but I have actually heard pilots brag about paying off schedulers to get good trips or not get called, as well as what kinds of things different schedulers like (this one likes pizza, that one chocolate). I refused to play the game, so I flew about 10 hours/month while on reserve, and got the call on holidays (I remember one memorable 4 July trip- one leg out of 30 minutes, spend the night, one leg back. That was all I flew that month.). Other pilots junior to me flew 80-90 hours.
2. Once you are off reserve, the amount you fly is based upon... you guessed it, seniority. The more senior you get, the more hours you can fly in a month with more days off. The junior schedules at ASA have you fly 75 hours with 10 days off; the senior lines have about 16-17 days off with 80-90 hours of flying.
There is something called "open time" at airlines. It is unassigned flying that can be picked up by pilots on off days. Again, the more senior you are, the better chance you have of picking up open time. You also have more off days in which to plug it in. The airline will not let you bust the FARs (30 hours/week, 100 hours/month, 1000 hours/year, one day off after working 6 days), so that junior pilot with only 10 days off has little chance of picking up open time.
It is very possible to "time out"- to hit your maximum hours for a week, month, or yes, even a year. I have known a few pilots who hit their 1000 hours of flying in late November/ early December. They are off with pay the rest of the year. NOTHING the airline can do. I have done it for a week several times, but never for a month. I prefer to spend time bothering my wife and chasing her around the house than spend time next to some ugly mug such as yourself.
Hope this helps. I think most other airlines are the same, as with the previous Skywest poster.