The main medical cause of snoring (at least the majority of the time) is that the airway in your throat constricts (shrinks) and so your body is not getting enough air when you sleep. The snoring is your body’s way of trying to naturally compensate. There are all kinds of machines, gadgets, gimmicks, medicines, and combination of all of the above that have been touting their ability to prevent a person from snoring, with mixed results. There are some people who have touted various methods to stop snoring without the use of any other assistance. According to these people, the problem is that your tongue gets in the way of the airway, and training the tongue to stay out of the way will eliminate the snoring. There are websites and even entire books touting this method.
Another thought is that literally 99% of people who snore breathe through their mouths at night. This has led to a relatively new idea, a chin strap. The idea behind this is that if your mouth is held closed when you sleep, you will have to breathe through your nose and therefore will stop snoring. Some people say that after a certain amount of time this will train you to naturally breathe with your nose at night, others do not make any type of similar claim. The obvious problem to this is how uncomfortable it can be.
There are various more conventional methods of dealing with snoring, which include various nasal strips (to open the breathing passages) and nasal sprays. There is also a specialized pillow, designed to relax and support the neck muscles in such a way that it is also supposed to keep the airway open and therefore reduce snoring. Some studies have also found that smokers who quit sometimes top snoring as their lungs recover. There are many different options and directions, but there is probably an option out there for anyone who wants to look.