Can an receiving team following a fair
catch go for a field goal and what it is
the mechanics for the officials to line up?

Larry- Yes the receiving team has the option to attempt a field goal after a fair catch. federation, rules line up just like an extra point with the back judge and line judge under the goal post. referee with the kicker, linesman on the kicking teams yard line(lime of scrimmage). umpire 10 yds away and on oppsite side of field. just like a kick off now. remember if the receiving team chooses to put the ball in play, and their is a penalty on the defense the offence can still request a free kick. hope i was able to help.