Officials initially signal fouls by tossing a bright yellow colored flag onto the field toward or at the spot of the foul. Because of this, broadcasters and fans often use the term "flag" to refer to fouls during the game.
During a play, multiple officials may flag the same play, and multiple flags may be thrown for separate fouls on the same play. If applicable, the same official can signal additional fouls on a given play by throwing a beanbag or his hat. When officials throw a flag during a down, play does not stop until the ball becomes dead under normal conditions, as if there were no fouls.
Once the ball is dead, or immediately when a foul is called after a play is over or prior to a snap (since the ball is dead anyway), the referee, the official(s) who threw the flag(s) and other officials with a view of the play confer to come to a consensus on whether an infraction was actually committed, what it was, and who committed it. The final determination and assessment of the penalty is the sole responsibility of the referee. The referee then makes initial visual body signals to the press box (and crowd) indicating what fouls were committed and the team that committed them, the latter shown by extending the arm toward that team's end zone.
The referee then confers with the offended team's on-field captain to find out whether the offended team would rather decline the penalty and take the result of the play. In certain situations, the result of the play may be more advantageous to the offended team, especially, for example, if time is running out in the half and a 7-yard gain is a better option than a 5-yard penalty. However, there are certain scenarios where the referee may not have to confer with the team captain because the enforcement is entirely obvious (such as a false start foul or other penalties called prior to the snap) or when the choice is fairly obvious (such as when the defense commits a foul during a play in which the offense scores a touchdown).
After any final conference, the referee then makes full visual signals describing the foul in detail, which consists of: the foul that was committed, the team that committed it, whether or not the opposing team chooses to decline it, and the resulting down or possession. In College football, the NFL and other professional leagues, and in some high school games, the referee also announces the fouls and their penalties over a wireless microphone to the members of the teams, the crowds in the stands, and viewers/listeners of the televised/radio broadcast of the game. In college and professional football, the referee will also give out the numbers of the players who committed the fouls. During these announcements over the microphone, the referee usually does not use names of the respective teams or their cities, but rather will use the generic terms "offense", "defense", "kicking team", "receiving team", etc.