Flush doors -- those with smooth, flat surfaces -- are easy to paint with either a brush or a roller, but doors with inset panels can be tricky. No matter what type of door you're dealing with, paint the entire door without stopping. Otherwise the lap marks may show. Before you start, remove the doorknobs, the plates behind them, and the latch plate on the edge of the door.
On ornate doors, start by painting the inset panels at the top of the door. As with wainscoting, paint all the panels and the molding around them. Then work your way down from the top to the bottom, painting the top rail, middle rail, and bottom rail (the horizontals) with back-and-forth strokes.
Next, paint the vertical stiles (the sides) with up-and-down strokes. If you're painting both sides of the door, repeat this procedure. If you're painting only one side, paint the top edge of the door with a light coat. Over time, paint can build up on the top edge and cause the door to stick. Finally, paint the door's hinge edge and latch edge.