A free kick is a way to start play again after some violation of the Law - a misconduct or a foul.  The free kick takes place where the foul or misconduct happened (see Special Rules #2 and #3 below)

A goal can be scored directly from a direct free kick but only against the opponents.  (Remember: "directly" means that no one else has touched or played the ball)
For any free kick, the ball is in play as soon as it is kicked and moves.  (see Special Rule #1 below)
All players from the other team must be at least ten yards away from where the free kick is being taken (see Special Rule #4 below)
The kicking team can decide to go ahead and take a kick anyway even if there are opponents closer than ten yards
An opponent who gets too close and interferes with or delays the taking of a free kick can be cautioned for misconduct and shown the yellow card
Not OK
The player taking the free kick cannot touch the ball again unless another player has touched it (an indirect free kick is given to the other team if this happens)
A goal cannot be scored directly from an indirect free kick (the ball has to touch at least one other player on either team before entering the net for the goal to count)
The referee signals an indirect free kick by raising an arm straight overhead.  The referee keeps the arm raised until the ball is touched by another player or leaves the field of play

It is still an indirect free kick even if the referee forgets to do this.
Special Rule #1
If a free kick is given to defenders inside their own penalty area, the ball is not in play until it leaves the penalty area.  All opponents must be outside the penalty area when the kick is taken
Special Rule #2
If an indirect free kick is given to the attacking team inside the defender's goal area, the ball is placed on the goal area line closest to where the foul or misconduct occurred
Special Rule #3
If a free kick is given to defenders inside their goal area, the ball can be placed on the ground anywhere in the goal area
Special Rule #4
Opponents can be closer than 10 yards to a free kick if they are standing on their own goal line between the goal posts