Schedules and seniority
Schedules are based on seniority, i.e. date of hire. If several people are hired on the same date, companies have various schemes to determine who is most senior of that class. Some places use birthdays. Others may use the last four digits of your Social. Still others may use class rank; obviously, if you are "valedictorian" of your class you'll be senior to the rest of your classmates but junior to the other pilots at your airline.
One you are qualified for the line, you'll receive paperwork to submit a bid on a line. You'll be taught sometime in ground school how to fill out and submit the paperwork. Once again, the most senior people win the "auction." You will hold the best line your seniority can hold. Usually the most junior pilots can only win reserve, meaning they are on call in case someone in their crew position calls in sick or something. You may be sitting reserve at home. I've heard that some pilots have to report to the airport to sit reserve for their shift. If you are allowed to sit reserve at home, you can roam about with your cellphone or pager, but you have to remain a certain distance or minutes away from the airport.
It varies from company to company, but you generally know your schedule a month or so ahead of time. Your schedule can change from month to month.
You start off at the bottom of the totem pole. You will be assigned the best aircraft your seniority can hold, which is usually the most junior equipment on the line. As your seniority number improves, you can bid better lines, more senior (and better) domiciles, and eventually more senior aircraft and crew positions.
One other aspect of seniority which is extremely important. Your seniority number can affect your earnings. If you pull a bad seniority number it may take you much longer to bid successfully for more senior equipment, if you want it, and you will have fewer years flying that equipment than someone with a better number.
These are the basics of bidding and seniority as I know them. There are variations to this theme. For example, some pilots have enough seniority to hold more senior equipment. However, it could mean that once they get that equipment they drop to the bottom of the list in terms of bidding good lines on that aircraft, e.g. reserve again. They may not think it's worth it because they are senior on their current airplane and are happy with the schedules they get.
Hope this helps, along with the other fine explanations above.