Open and close the door, paying attention to where it begins binding. Look for scuffed paint or other signs of rubbing along the sides and top of the door.
Tighten the screws in the hinges of the door with a screwdriver. This helps the door stay level and secure so it doesn't rub due to improper hanging.
Use a chisel to carefully remove the paint that is built up on either the door itself or on the door frame so that it doesn't get in between the door and frame to cause binding. Sand along the edges where you removed the paint to smooth them out.
Sand some of the wood off of the door if excess wood is the cause of the binding. Start with a coarse sandpaper, focusing mainly on the hinge side of the door. Sand along the top as needed to help the door fit better. Move down to a fine-grain sandpaper to smooth out the wood once you remove enough of the edge of the door with the coarse paper.
Mark the hinge edge of the door in the areas where the door is rubbing while the door is still hanging up. Plane the door in those areas, shaving along with the grain, taking off only a small amount of the door at a time. Test out the door before planing off more of the door.
Sand the edges of the doors with a fine sandpaper to create a smooth finish. Rub paraffin or paste wood lubricant along the edges of the door. Both actions will help prevent rubbing and binding.