If you mean by "blight" the fungal disease, Early blight, it is spread by splashing water, and sets in early in the season. Early blight produces a wide range of symptoms at all stages of plant growth. It can cause damping-off, collar rot, stem cankers, leaf blight, and fruit rot. The classic symptoms occur on the leaves where circular lesions up to 1/2" in diameter are produced. Within these lesions dark, concentric circles can be seen. The leaf blight phase usually begins on the lower, older leaves and progresses up the plant. Infected leaves eventually wither, die, and fall from the plant.
Many times the tomato plant can out-race the disease and you can still get tomatoes off of the plant. If they are severely effected you may want to discard the plants altogether. For management information read: Tomato Early Blight.
In addition to blight, there may be other problems with your tomatoes. The dark circular area on the bottom of the tomato fruit is blossom end rot, a problem caused by inconsistent watering, or calcium deficiency. Make certain that you water on a regular schedule. If the spring has been cool, tomato ripening may be delayed by several weeks. For more information on growing tomatoes read: Recognizing Tomato Problems
