How long would it take to fix my snaggle tooth? (Photos)

Ideally by age 8 you would have had your jaw expanded when it was very easy.  As an adult the best approach is a removable functional appliance to grow your maxilla orthopedically.
This will eliminate dark buccal corridors and make room for all of your teeth.  You are 19 and deep nasal labial groove are already present.  This will develop a full wide natural healthy looking 10-12 tooth smile.
The Sarpe procedure is an alternative route.

Both procedures will improve your airway.

Ira L Shapira DDS, D,ABDSM, D,AAPM, FICCMOPast Chair, Alliance of TMD OrganizationsDiplomat,  Academy of Integrative Pain ManagementDiplomat, American Board of Dental Sleep MedicineRegent & Fellow, International College of CranioMandibular OrthopedicsBoard Eligible, American Academy of CranioFacial PainDental Section Editor, Sleep & Health Journal
Member, American Equilibration SocietyMember, Academy of Applied Myofunctional SciencesMember, Academy of Cosmetic Dentistry

Your dental arches are grossly underdeveloped; this is why there is no room to properly align your teeth. The best way to resolve your problem is to first enlarge your dental arches and then straighten your teeth.Enlarging your dental arches is done with a removable appliance and would take approximately 12 months. Straightening your teeth would could be done with fixed braces or removable aligners and should also take approximately 12 months.Straightening your teeth without developing your dental arches first would require extracting teeth which would cause a myriad of future problems. Developing your dental arches would not only give you the necessary room to straighten your teeth but would also make your smile much broader and prettier and would also improve your TMJ and airway health.Good luck!