Before requesting a substitution, the coach should have identified the players to go in, and have them ready to enter the game from the half-way line.
At an appropriate time, get the referee's attention, usually by yelling "Sub Ref".
AFTER receiving permission from the referee to perform a substitution, call off the players who are to be replaced. Unless the referee tells you otherwise, the players should exit the field at the half-way line on your side of the field.
You may send on replacement players ONLY after the referee gives permission for them to enter the field. Note that the FIFA laws of the game require that a player may not enter the field until AFTER the player they are replacing has left the field. In youth matches, especially younger youth matches, a referee may give permission for the replacement to enter the match before the player they are replacing has completely exited the field. This helps speed youth matches in which there are many subsitutions. However, the referee is not required to do so, and if substitutions get 'confusing' may certainly require that the FIFA laws of the game be followed.
If you are changing goalkeepers, you should specifically inform the referee that you are doing so. This is normally done by yelling "sub ref". Then, when the referee gives permission for the substitution to begin, the coach would yell "keeper change" or some similar phrase to inform the referee. Changing goalkeepers, especially in younger youth matches, may require additional time as equipment is changed. Advising the referee that a goalkeeper change is happening helps make sure the referee doesn't restart the game while the new goalkeeper is struggling to put on equipment.
Within Washington State, referees are empowered with the authority and responsibility to remove from play any player that they "suspect may have a concussion". As most referees are not physicians, and since proper evaluation of a head injury actually takes some time, most referees upon seeing a potential head injury will ask the coach to remove the player and conduct an evaluation. The coach must cooperate with the request. However, if the referee sees clear symptoms of concussion, the referee MUST REQUIRE the player be removed and MAY NOT permit the player to reenter. In this case, referees are advised that they must capture the identity of the player and report the matter on their match report. Per Washington State Law, the player may not participate further until they have received medical clearance. In the interest of player safety, coaches and referees must cooperate to promptly remove any player that may have suffered a concussion from risk of further injury. Therefore, if a coach is aware of a head injury that requires removal and evaluation that the referee may not have seen, the coach should immediately call this to the referee's attention so that the player may be removed.
Note that all substitutions are made only with the permission of the referee. Just because you are permitted to sub at a time, does not mean the referee must grant permission. The referee should not permit a substitution if so doing would interrupt the flow of play. Teams may wish to take a "quick kick" when they are awarded a direct free kick, or may be advancing the ball down the touchline with a series of quick throw-ins. Those would not be good times to stop play and permit substitution.
Coaches are also reminded that the game of soccer is intended to be played with few stoppages. While recognizing that coaches have an obligation to their players to give them an appropriate amount of playing time, frequent substitutions with the tactical objective of slowing down the game or wasting time are inappropriate.