Just based on the few photos above, it seems like your best starting option would be orthodontics to move the teeth into the proper position. This would improve your bite and set the stage for any future restorations you need. Definitely consult with a dentist--it important to review xrays as well to rule out an periodontal/bone issues.Good luck.
Cosmetic Dentistry and Closing spaces
From the photo it appears you have what we call and end to end bite. If this is the way the teeth do meet together, then consider some type of bite correction, perhaps orthodontic care. Any chance you have a tongue thrust that is causing the teeth to splay out? If so, airway issues are the usual cause of this. Bonded, veneers could be used to help improve your smile, more so on the upper than lower as placing a conservative type of bridge to add a tooth will result in no midline for the upper and lower teeth. Best bet seems to be to see why your teeth are splaying apart and perhaps consider orthodontic care.