The 90 minute rule states that teams have a right to use the field for 90 minutes from the scheduled kick-off time.  At the end of 90 minutes, the field is to be available for the next group of players. 

You, as referee, have to make sure that this happens.  It's part of game mangement. 

You are expected to do everything possible to get the two teams ready to start at the scheduled kick-off time.   This is often easier said than done, but do what you can.   You should be at the ground in plenty of time - preferably 60 minutes but certainly no less than  45 minutes before kick-off.  You should be changed and ready to roll no less than 15 minutes before kick-off time.    Boot check, coin toss, game sheet, etc. can all be done before the field is available.  Tell the teams that you expect them to be ready to move onto the field as soon as it is available.   If they are not in match kit 10 minutes before kick-off, remind them again.

The League Regulations require matches to begin on time.  Contrary to some people's opinion, there is no 10 minute grace period.  In fact, if one team does not have 12 players on the field at the scheduled kick-off time, the other team can claim a win by default.  This is up to the teams.  The referee should be prepared to act as witness but should not instigate any default claim. 

If, despite your urgings, the match starts late, calculate the time available and adjust the length of both halves to suit.  With 40 minute halves and 5 minutes half time, 90 minutes is just long enough.  If you are 10 minutes late kicking off, reduce both halves by 5 minutes and you should be OK. 

The only extenuating circumstance is a major injury requiring wait time for an ambulance.   Discuss the situation with the team captains and the officials for the next match (if any).   Reach an agreement regarding timing and communicate the decision to all affected parties.  For minor injuries, the playing time in the half should be adjusted so that there is no overall time extension.

All this is just good manners.   There may be players on the team who have to rush to jobs after the match.  There are players and officials in the next match who are warming up and expect to start on time.  There are spectators who expect a 3 pm kick-off, not one about twenty minutes later.  

If hockey can do it with "ice time", Rugby can surely do it with "field time".     Game management begins before the first whistle.  Be prepared to play your part.