Step One: Say The Vowels
Repeat all the vowels, A, E, I, O, U, for two minutes in front of a mirror. Try to over-enunciate and watch how your mouth and jaw move to get a sense of the different muscles you're using to make each sound.
Do this for two minutes.
Step Two: Strengthen Your Tongue
Keeping your tongue strong is important, as this will prevent it from falling backwards and blocking your airways when you're asleep.
To get it in fighting shape, slowly move it towards and away from the back of your front teeth. Repeat this for a few minutes, making sure not to clench your jaw in the process.
Step Three: Work Your Throat Muscles
This is the exercise that will likely feel the strangest, but will also give you awesome results. Contract your throat muscles for about 20 seconds in front of a mirror.
To ensure you're doing it right, check to see if your uvula is moving up and down. Repeat the cycle for as long as it feels comfortable.
Step Four: Condition Your Jaw
To strengthen your jaw, gently let your mouth drop open. Then, move your jaw slowly to one side and hold it there for 20 seconds. Next, return your jaw to its normal position and close your mouth. Do the same thing on the other side, and continue the cycle for 1-2 minutes.
Repeat this sequence as necessary, and aim to build up to doing it multiple times a day (especially before bedtime) for faster results.