Why do my tomatoes turn black on the bottom before they are completely ripe,and what can I do to correct the problem?

Are the bottoms touching the ground?
I noticed when I pick tomatoes the ones that are on the ground turn black where the ground was touching it.
Also you could try turning them so they are not sitting on the same spot.

I used to spread straw around each plant and that stopped the black 'damp' spots. Better idea is to use the cages so the fruit doesn't touch the earth.

Too much water too late in the evening?

Blossom end rot, perhaps?
Managing Pests in Gardens: Vegetables: Environmental Disorders: Blossom end rot—UC IPM (http://www.ipm.ucdavis.edu/PMG/GARDEN/VEGES/ENVIRON/blossomendrot.html)
Managing Pests in Gardens: Vegetables: Tomatoes—UC IPM (http://www.ipm.ucdavis.edu/PMG/GARDEN/VEGES/tomato.html)

Classical symptoms of blossom end rot check nutrional state esp calcium