Black teeth, how to fix? (photo)

The dark areas in between your teeth are either heavy staining, discoloration from decalcification or decay (cavities).   Your dentist should be able to give you an idea for treatment needs and cost. 

The black lines between you teeth looks like stain or leakage around existing old white fillings. 

An examination by your dentist and some x-rays can reveal for sure if it's stain or leaky fillings. Either way the fix may be as simple as replacing the old fillings!