Cut the black spots off and eat them.

After they ripen, of course.

Seriously, the black spots can be from several causes, but the most common is a combination of irregular watering and a lack of calcium, which is usually evidenced by "blossom end rot" - a really ugly blackening of the tomato bottom (frankly, I don't eat those maters cuz they don't taste as good to me!). BER is best controlled by irrigating deeply and regularly -- and not muttering to ancient spirits regarding excessive and inopportune rainfall, because planting tomatoes in a calcium-enriched and very well-drained soil is usually sufficient to balance the summer storms.

Bacterial speck and Bacterial spot seem to occur during periods of high humidity and/or frequent rains/mists; the bacteria overwinter in ground debris. The spots are usually smallish and look rather like tiny rotting freckles. If it spreads it can ruin your crop (or at least make it look yukky), so practice good cultivation to include removing and hot-composting the mulch from around any infected plants (replace with fresh mulch, of course). The infected tomatoes can be used after trimming off the spots, but don't put the trimmings into the compost.

You might find link helpful.

Here is a link that might be useful: tomato FAQs

To be clear on info in this thread. This is my first year with a garden and I have 4 beautiful plants, but clearly have bacterial spot that has now spread to almost every single fruit on the plants (with the exception of a couple of cherry tomatoes that are still spot free). All others have tiny brownish to black specs. My primary use of my fruit will to be to peel and seed the tomatoes for sauces. Can I still do this with the fruit that shows the spots. I have young children and want to be sure that the bacteria that causes the spots is not going to make anybody ill. Thanks...