Typically, mouthguards are only intended to go over the top teeth, since this provides some protection to prevent you from scratching or injuring your lower teeth. However, under some circumstances, the dentist may design a mouthguard for your lower teeth. These are also used to shield people who have braces or other dental equipment. You should consult with your dentist to determine the right course of action for you.
When you get your mouthguard(s), make certain that they fit properly. A mouthguard should be simple to insert, easy to wear, and should not impair breathing or ability to talk. Mouthguards should be sturdy, tear-resistant, and easy to clean.