Pruning tomatoes can help increase the size of the fruit you harvest and can help keep your container tomatoes from getting out of hand. Pruning tomatoes is not necessary for all types of tomatoes, though, so knowing which cultivar you're growing can be the difference between a bumper crop and no crop at all.
Find out whether you have determinate (bush-type) tomatoes or indeterminate (vine-type) tomatoes. Determinate tomatoes will generally not require pruning--in fact, if pruned incorrectly, they will stop growing and produce little or no fruit.
Remove the suckers up to the first cluster of fruit if you're growing determinate tomatoes. Wait for the suckers to grow two leaves above the first fruit cluster, and then pinch off the tip. Suckers are the shoots that grow from the angle between the large leaves and the main stem. Eliminating suckers will reduce the number of fruit your tomato plant produces but will increase the size of the remaining fruit. This should be the only pruning, if any, you perform on a determinate tomato cultivar.
Use a cage or stake to support your plant if you're growing indeterminate tomatoes.
If you stake your tomatoes, remove all but one sucker at the base of the plant. The sucker you leave will become a second main stem. The best time to remove the suckers is when they're three to four inches long. Continue pruning suckers from the main stems weekly. The remaining two stems will produce a lot of flowers and fruit.
For caged tomatoes, you can leave three or four main stems close to the base of the plant instead of one or two. Other than that, the process is the same as for staked tomatoes.