In order for a player to be eligible for the NFL draft, at least three years must pass before he's left high school. This means that almost every player selected on draft day has spent those three years playing college football, but occasionally players are drafted from other leagues like the Canadian Football League, Arena Football League or other sports like rugby. This is in contrast to other sports like baseball, where players can be drafted at any age, and to the NBA, where players need only wait one year after leaving high school to be drafted.
The NFL draft is designed so that the teams that were worst in the past season have priority in selecting the top players that are eligible that year. All of the teams that weren't in the playoffs pick 1-20, while the rest of the teams pick in order of which round they were eliminated in the playoffs, in addition to a group of other criteria. The Super Bowl winner always has the 32nd, with the loser getting the 31st.
Among all of the teams drafting, the draft order goes in reverse order of their win and loss record. If teams have the same win and loss record, then the relative difficult of their opponents (i.e. "strength of schedule") determines who picks first. For example, imagine that at the end of the season one team had a 1-15 record while two teams had 2-14 records. In this case, the 1-15 team would have the first pick of the draft, and who had the worse strength of schedule (i.e. played worse competition) picks second. The overall order is maintained through all of the rounds of the draft, with only a few exceptions.
Starting in 2010, the NFL Draft began to take place over the course of three days. On the first day, the draft consists of only the first round, in which each team has 10 minutes to make its pick. The second day consists of rounds two and three, and the amount of time for each pick falls to seven. On the third and last day, rounds four through seven take place, and each team has five minutes for its picks.
One of the most exciting elements of the NFL Draft is trading. At any point in the draft, a team can trade some of its picks for the rights to current NFL players, other picks in the same draft or picks in future drafts. This can create quite a chaotic atmosphere, especially when teams have their eyes set on specific players and give up too much to get them on their teams.
Generally through the first round, the amount each new rookie gets in his contract decreases. The amount each player earns is roughly based on a combination of what the player at his draft spot in the prior year received, with the player's position taken into account. While NFL contracts are not guaranteed, one of the most criticized elements of the draft is how much unproven players are paid, as quarterbacks picked at the top of the draft can get contracts in excess of $50 million.