Tomatoes leaf spots will be starting on the lower leaves and working their way up the plant. The main cause of this is fungi causing Septoria, early blight, and late blight. These are worse in wet, humid weather.
The best cure is prevention. The spores exist in the soil and are splashed on the lower leaves first. So, rotating your plants from one side of the garden to the other helps. Pruning off the lower leaves and growing the plants off the ground in cages or stakes.
The best help I have found is growing the tomatoes with a mulch like plastic, fabric, or organic (old rotten hay or straw). Use grass clippings sparsely for they tend to mat down and get hot if used too thickly. If you have treated the grass with an herbicide, do not use it.
Do not spray the plant with overhead sprinklers. Try to use a form of drip irrigation so the leaves do not get wet.
You can regularly use an all-purpose garden fungicide to prevent non-affected leaves from infection.