What are the tiny white bugs on my tomatoes?

Sounds like you have aphids. Washing them away is the best method for control, but you have to be very persistent, and consistent, washing every day, possibly several times per day....and don't forget the undersides of each leaf. Just use a mild dish soap (I do not recommend Dawn!) and warm water, then blast the bugs off with a good, hard spray from your garden hose. Additionally, I strongly recommend neem oil as a topical spray, and systemic treatment until the fruit is set. Once the fruit is set you don't want to use anything systemically within a couple of days of picking the fruit for eating or you'll taste the neem oil.

Some sites will give you all kinds of warnings about neem, but I'll give you a link to find information about it's actual safety. It's entirely organic in and of itself. The problems with most neem products is that there are additional ingredients that can be harmful, and not organic. Just use straight neem oil in warm water in a spray bottle and spray it directly on the plant once per day between washings. For the systemic treatment, put about a quarter of a cup of neem oil in a small bucket of warm water, mix real well, and dump it at the base of the plant ...then just don't give the plant MORE water....it'll get enough from this treatment while you're doing it. Next year, don't plant tomato plants in the same spot. Plant some nasturtiums and or marigolds there instead, and always plant those near your tomatoes! Also, if you don't already, you should look into companion planting. Some plants attract bugs to other plants, and detract from plants, etc., it's a very good method for controlling pests.

http://neemresource.com/

http://neemresource.com/AboutNeem.html

Great thank you! I will try your suggestions. My one plant is full of tomatoes but they are still small. Im in the woods so i have very limited spaces for sunshine. I've been planting in giant pots. Where i have them this year i was thinking of putting a green house next year. Would it help if i floored or tarped the ground there?

Beth63 has good information. You also might plant marigolds. I don't care what arguments for or against them there are, they do work, and they worked for our family.