I can't comment as to the Coptic Church, but here is what Armenians do:
Upon entering the church:
1. Cross yourself when you enter, if you find that you have to cross the middle to get to an open pew, turn facing the altar and cross yourself again solemnly while bowing your head, then move to your pew.
2. When you find your pew, cross yourself, say the Our Father, cross yourself again and sit down (if you are allowed to at the point in the services).
Upon leaving the church:
1. Stand in line to kiss the Gospel and say (Hishestse Der zamenayn badaraks ko, "May God remember all of your sacrifices").
2. As you move towards the exit, take the mas (post-communion bread).
3. You must exit the door walking backwards, and cross yourself, so as not to "turn your back on God".
Maybe it is similar in the Coptic Church?