How to plant your tomatoes really depends on how you plan on tending them throughout the growing season. If you are planning on pruning out the suckers and keeping a couple trellised, tidy main vines, then you can plant them closer together. I plant mine about 18″ apart in this case.
If you have no intention of keeping your tomatoes pruned, or are the type that starts off with good intentions but then loses interest, I would plant them farther apart. About 3 feet. This leaves you plenty of space for air to move through your plants. Which means the foliage can dry out more quickly, lessening your chance of disease.
Either way, when planting I carefully bury at least half of the stem leaving only the first few sets of leaves above ground. Make sure those sets of leaves are not touching the ground. I then mulch heavily around each plant/row with straw or grass clippings. By heavily I mean about 5 inches of mulch. Mulching helps keep a more even moisture level and keeps the soil from splashing up onto the leaves, lessening your chance of disease.
Water in well. If you plan on laying soaker hoses do so before you add mulch. Placing the hose just a few inches away from the plants base.
Make sure you provide some kind of strong support for them right away as it gets hard to add once the plants begin to grow.
Side note: I use all my extra cherry tomatoes to make sauces! No need to peel, I just use my immersion blender to blend them up while they’re cooking. Chef’s tip… roasting your tomatoes in the oven before adding them to the pot helps reduce cooking time and gives your sauce incredible flavor!