When are teams allowed to make make substitution?

I am a new referee at the Recreational level. I am confused as to when teams are permitted to make substitutions. Having heard conflicting responses from the referees I work with, I want to ask the question on here, because I am serving as central referee for the first time this weekend. I could not find a clear answer in the publications “Laws of the game,” or “Guide to Procedures.” However, a common pattern of answers where I work is that you can sub at most stoppages but not during corner kicks or opponent throw-ins. Yet other claims are that you can only make subs when the restart is in the advantage of your team. If you could clear this issue up for me, I would be very pleased and would educate refs and coaches alike in my league.

Thanks in advance for your help!

USSF answer (April 30, 2009):
Actually, you will find the procedure for substitutions in two separate places in the Laws: In Law 3 (The Players) itself and in the back of the book, under Interpretations and Guidelines for Referees. We include here only the latter, as it is more complete:
Substitution Procedure
- A substitution may be made only during a stoppage in play
- The assistant referee signals that a substitution has been requested
- The player being substituted receives the referee’s permission to leave the field of play, unless he is already off the field of play for reasons that comply with the Laws of the Game
- The referee gives the substitute permission to enter the field of play
- Before entering the field of play, the substitute waits for the player he is replacing to leave the field
- The player being substituted is not obliged to leave the field of play on the halfway line
- Permission to proceed with a substitution may be refused under certain circumstances, e. g., if the substitute is not ready to enter the field of play
- A substitute who has not completed the substitution process by setting foot onto the field of play cannot restart play by taking a throw-in or corner kick
- If a player who is about to be replaced refuses to leave the field of play, play continues
- If a substitution is made during the half-time interval or before extra time, the process is to be completed before the second half or extra time kicks off.

You will find, as you progress up the refereeing ladder, that many competitions (leagues or tournaments, etc.) make up their own rules for substitution, many of them not quite in agreement with the Laws of the Game — the Laws allow for different rules only for players below the age of 16, “veterans” (over 35), female players, and disabled players. If you accept a game in such a competition, you are bound to follow their rules.

Most of the local substitution rules are at least partly consistent with the Laws of the Game, but are valid ONLY if the players are below the age of 16, veteran (over 35) or female footballers, or disabled.