Now that your tomatoes are growing like weeds it is time to prune out the suckers. The advantages to pruning out the suckers on your tomatoes are increased fruit size, better air circulation, which will help with disease prevention and earlier fruit development. The suckers are the stems growing out of the leaf crotch. You should remove the suckers from the bottom of the plant up to the first flower cluster. Remove them before they get too big, less than 2-3” long is a good rule of thumb. You will need to keep an eye on your tomato plants throughout the season and prune the suckers as they get big enough, look for new growth coming up at the ground too and cut those out. Also you want to remove the yellow or dead leaves (especially seen on the bottom of the plant). Only prune the indeterminate varieties; determinate varieties should not get pruned, you can leave the suckers on those plants.
If you are supporting the plants with an overhead trellis with string or wire supported at the top you can allow your plants to develop two leaders or more commonly, it is pruned to a single leader. Prune out suckers along the plant to allow for better air circulation and less weight. You will have a reduced yield, however, the tomatoes that are left will develop earlier and will be bigger. Read the whole article on tomato pruning.