I have been through many years of speech therapy, but all the therapists and doctors I have seen over the years have given me some form of mouth exercises. Some exercises have stuck with me over the years. Most are to help with coordination and strengthening of the lips and tongue, which helps make speech more intelligible.
Here are some exercises that you might try. Do them in front of a mirror so you can be sure your mouth is straight and not to the side:
1) Press your tongue on the side of the cheek and hold for 5 seconds, gradually building to 30 seconds.
2) With your tongue, try to touch your nose and your chin.
3) As quickly as possible, go from a smile with teeth showing to closed lips.
Note: With this exercise, you might need a therapist or someone who is familiar with speech therapy to observe and make sure you do them correctly. I can tell you from experience, once you learn to do them wrong, it is hard to relearn them correctly (that is with everything).
4) Make the B, P, M sounds (closing lips).
5) Make the S sound.
6) Make the CH, SH sounds.
7) Vowels are the most important letter to correctly sound out. Practice A, E, I, O, U.