How to fix my asymmetrical smile? (Photo)

No one is perfectly symmetrical and rarely do the right and left sides match like a mirror image. That being said, porcelain veneers are the best way to balance and harmonize your smile by providing more symmetry.
You ask a really good question by wondering why your smile is asymmetrical, is it the teeth, muscles or something else. Everyone situation is unique and different, however in your case, it looks like its a combination of factors. From your pictures, it appears as if your face muscles pulling are pulling a bit harder on your left side, showing more lower teeth. It also looks like your left teeth are a little longer. Many times we see right handed patients with longer teeth on the left. This can be caused by improper teeth brushing, we usually see the opposite problem in left handed people. 
One other issue I can see from your pictures is the color difference between your canines and other teeth. This is not uncommon as canine teeth are made up of thick enamel that makes them look darker at times. Veneers will fix this issue as well as the porcelain will make all of your teeth the same color.
I would recommend a minimum of 8 to 10 porcelain veneers to fix all of the above mentioned issues. In addition to balancing your smile, the porcelain can balance the color as well. Veneers are thin shells of porcelain that are bonded onto the front surface of your teeth. Your are an ideal candidate for minimal prep veneers as your teeth appear to be straight and in a good position. 
See and expert cosmetic dentist and they can show you all of the possibilities. 

a third option would be to see an orthodontist to get the bite better to close those spaces on the left side.  nothing is as strong as natural teeth, so if you like the color and size and shape of your teeth, an orthodontist, either with invisilign or traditional braces (may be faster), can move the teeth to be symmetrical and you be happier with your more balanced bite and smile.

Hi:From the photos it appears that the teeth on your left side are a bit longer and more gum is showing.  If you are happy with the color of the teeth, then a simple solution would be to shorten the teeth on the left side with enamel recountouring and change the level of the gum with laser gum recountoring.  Consult with an experienced cosmetic dentist.Best,Dr. Maddahi