Everything at an airline is based upon:
1. FAR 117
4. Crew scheduling
What I will write applies to my airline but probably applies to most.
1. As a reserve pilot (what you will be as a new hire), you can't bid on open time. You can put yourself in the "fly" list meaning you want to fly. Some good trips go to reserve, but many are crappy- DH (dead head),to KCHA, spend 24 hours on the ground, 1 hour trip home. I really had one of those as a junior FO.
2. Once you hold a line there are a few types of trips you can pick up. "Open time" which are trips the company does not have covered. Sometimes the company will have an added incentive for picking up the trip if they do not have reserve coverage- otherwise they might have to draft someone.
Crew posted trips. These may be trips other crew members want to swap or drop. They may want to drop all or part of a trip. I post all of my trips in open time each month then fly what the vultures leave. About 9-12 days a month.
If a trip fits those things I numbered above you may pick it up or swap it for a trip on your schedule.
3. You are payed a "guarantee" each month, usually about 75 hours of credit at most airlines give or take. Note I wrote credit, not hours. They are different. You can have 75 hours of credit with 70 hours of flying.
Take the pay rate, multiply by the guarantee and that is what you are paid each month unless your credits go over guarantee. You are also paid per diem which is based upon your TAFB (time away from base) verses flight time, and is normally about $1.50-$2.00/hour. This can add up over the span of a month as is tax free if the trip is an overnight trip.
So say as a junior FO you are awarded a month with 60 hours of credits- you are paid for 75 hours. Say you pick up a trip worth 12 hours of credit. 60+12=72. That is still less than 75 hours so even though you worked more you are still paid only for 75 hours (though you will earn more with per diem).
If you go over your guarantee you now earn more.
How much if any you want to pick up is a personal question based upon finances and life. My wife is a surgeon and this is my daughter's senior year. It needs to be a pretty sweet trip for me to pick it up even at my 700/900 captain rate. First year FO commuting- maybe not worth it. But your call.