I was always taught to sucker my tomato plants. What are suckers, you ask? Well just look at my little tomato here. The sucker is the shoot in the elbow of the plant, where the branch and the main stalk come together. How do you sucker? You just pinch that little shoot off. That's it. Now, there are pro's and con's to suckering. I generally sucker once, then let the plant go. Inevitably, my plants will have some suckers that progress, but when the plant is beginning to develop, I like to sucker so that it can give more energy to nice development rather than being just a big plant. What do I mean? Well, my mother-in-law hasn't always been a sucker remover. She grows gorgeous tomato plants. Unfortunately, in years past, the huge plant that she grew yielded very few tomatoes. It was an enormous plant.
Suckering seems to have helped some tomato yield whoas that I've had. I've also suffered from overwatered tomatoes (in a planter box) that developed blossom end rot. I've had an underwatered tomato plant that, when the blooms developed, an elbow formed and the plant dropped the bloom along with about a 1" "arm" of plant. Give the tomato enough water and it doesn't do that. After the underwatering was corrected, that same plant (an heirloom non-GMO Brandywine) had to be supported by 5 tomato cages and gave me 66 tomatoes from one plant. No, I'm not kidding.
Suckering tomatoes? Works for me. Others will argue against it. It's all good. Whatever makes your green thumb happy.