This is called Blossom-end rot, and can be treated with mixtures including epsom salts, among other treatments. There's a problem absorbing calcium. Tums crushed in the soil can also work!
The problem usually appears in the spring, perhaps you have planted your tomatoes too soon, before the soil has been properly warmed. Crowded conditions in your garden may contribute to black rot.
Tomatoes on vines with black bottoms are a result of too much watch. To avoid this,provide a soil with good drainage and monitor the moisture the plant gets. Any clay should replaced with loamy soil or other organic matter like peat moss. Adequate moisture is about one inch a week from all sources (rain, watering, etc.
Tomatoes getting to much water either from the weather conditions or too much watering will develope rotting on the bottom of the fruit. There is a spray commonly called "blossom rot" that will prevent this from happening.
This is called blossom end rot. It's a nutrient deficiency caused by a lack of calcium, possibly made worse by uneven watering. Your plants will probably improve as they grow.