Among the easiest and most effective ways to weatherstrip a door is this straightforward process:
1) Cut a short strip of cushion-vinyl or spring-metal weatherstripping, sized to fit against the door stop, behind the latch area. The illustration shows cushion-vinyl weatherstripping, but spring-metal (also called spring-bronze) works the same way.
2) If necessary, bend or trim this so that it doesn't intrude on the latch mechanism. Attach it with brads.
3) Measure and cut lengths of weatherstripping to fit along the latch side of the doorway, and then measure and cut weatherstripping for the top of the jamb and the hinge-side jamb.