Vine tomato plants need to be grown on a trellis to keep them off the ground. The reason for this is to keep the fruit away from animals and allow air to circulate so that they don't develop mold growth. Trellising tomato plants keeps them healthy for harvest, and the tying of vines does not take a great deal of your time, but other things must be considered as well, such as pruning.
Choose the type of trellis you want to use. There are many types. Basically you just need something with stakes and cross-sections. Size will depend on the number of plants you are growing. A single stake is all you need for a single plant. Something wider will work better if you are planting several.
Hammer the stakes of the trellis into the ground and make sure it is stable. In some instances, depending on the type of trellis you use, you might need to do a little more setup such as weaving wires between stakes or tying twine between the stakes for the cross-sections.
Plant tomatoes at the base of the trellis and wait for them to sprout up to reach the bottom rungs of the trellis.
Tie untreated twine loosely around the bottom of the plant and bottom of the trellis. This is used to stabilize the plant. Unwind the twine until you have enough to go a foot or more above the trellis. Tie the loose end of the twine to the top of the trellis so that it can be undone easily.
Untie the twine at the top and wrap it around the plant as it grows taller. This secures it to the trellis. Retie the excess back at the top. Repeat this as the plant grows so that it doesn't tear loose and fall over.
Trim growth as vines grow off the main stem. Wait until a side growth, or sucker, has three branches, then snap off the tip so the sucker doesn't grow anymore. The plant will grow upward this way instead of spreading out.