Why not try three different triggers rather than using one ?

If you insist on making just one trigger based on all events, here is what you can do inside the trigger:

IF EXISTS(SELECT * FROM inserted) AND EXISTS(SELECT * FROM deleted)

BEGIN

EXEC PROC_FOR_UPDATE

END

IF EXISTS(SELECT * FROM inserted) AND NOT EXISTS(SELECT * FROM deleted)

BEGIN

EXEC PROC_FOR_INSERT

END

IF NOT EXISTS(SELECT * FROM inserted) AND EXISTS(SELECT * FROM deleted)

BEGIN

EXEC PROC_FOR_DELETE

END