Remove the door from the door frame using a slot screwdriver on the hinges, then use a standard screwdriver to remove the hinges still attached to the door. This prevents the hinges from getting paint on them during the painting process. Remove the doorknob, door knocker and peephole -- this also requires a screwdriver. Put a tarp beneath the door as you paint.
Use a caulk gun and a putty knife to caulk and putty cracks and holes in the door, and use fine sandpaper to remove old paint chips and to sand down the caulk and putty once it's dry.
Purchase exterior primer from the hardware store. Prime all visible sides of the door, including the top, bottom and the right and left edges. Wait for the primer to dry. The paint should be an exterior-grade glossy paint. If you still have some leftover original paint, use that. Otherwise you need to color-match to a new paint. Paint at least two coats.
Paint rollers work well on flat doors, but most front doors have panels. You need paintbrushes, perhaps a small paint roller, and an angled sash paintbrush for painting corners. Start from the top and work your way down, eliminating drips as you go.