The trim around a door is called casing; is that what you are talking about? I don’t know where you would use coped joints on that. But then, I never cope joints anyway.
To set casing around a door, cut the two side pieces with a miter on top, fasten them in place, and fit the top piece. Then fit the base molding up to the casing side pieces. Really very simple; I can usually do it in about 15 minutes, if I don’t rush it.