The Container: Most tomato varieties want a large container. 15 gallons minimum. A tall pot is better than a short wide one. Don't skimp on the size of container, those roots need room! There must be a hole in the bottom for water drainage. I don't like those saucers that catch water under the pot. What's the point of a drainage hole if the pot is going to sit in a pool of water? Also remember that pots, especially dark plastic ones, can absorb a lot of heat. That's a plus in the spring when temperatures are cooler, but bad when it gets hot and the sun is intense. Draping shadecloth around the container will help. Thick terracotta pots don't seem to have this problem.
The "Soil": Container growing is not like growing in the ground. Do not use garden soil, topsoil, or that pile of dirt in the corner of your yard. The pot serves up some challenges, and using soil makes those problems worse. Don't use pure compost either. Use potting mix. A good one. Why? I could write a whole missive about this and tell you greenhouse horror stories involving 1000 tomato seedlings, but that's for another time. So, what's a "good" mix? Good mixes have structure, hold a lot of air and some water, but drain really well. Typical mixes in our area contain partially composted fir bark or bark fines (sometimes rice hulls), peat moss or coir, perlite, and some nutrients and ph adjusters. It's hard to recommend a brand, because I've had great results some years and bad ones the next with the same brand. Cynthia Sandberg, who farms for Michelin rated Manresa restaurant, swears by Gardner & Bloom potting soil. That's the best I can do for a brand recommendation. If you open a bag of potting mix and most of the contents are very fine (less than 1/16"), you don't have a good mix. It won't have enough structure, won't drain well, won't hold air, and will "collapse" or compact in short order. All bad news.
Planting: Tomato plants benefit from planting deeply. Very deeply. You want to bury much of the stem, I'd say halfway up the stem is good general rule. Clip off all the leaves below that halfway point just before you plant. The part of the stem that's buried will grow roots, which will produce a healthy productive plant. Before you place the plant down into the container, gently pull the rootball out at the sides, so it loses the seedling container shape and encourages the roots to grow outward. Once planted, water thoroughly. You want the potting mix and the rootball to get evenly moist. Just because water drains out the bottom doesn't mean everything is evenly moist. Water once, come back in 5 or 10 minutes and water again, then wait another few minutes and water a third time.
Nutrients: If you're using an organic potting mix, or one that does not contain a CRF (control release fertilizer), your greedy, hungry tomato plant will use up all the available nutrients in 4-6 weeks. I like to mix an organic dry vegetable food (such as Dr. Earth, Whitney Farms, Espoma, etc) into the upper 2 - 4" of potting mix at planting time with a little extra bat guano or alfalfa meal, used sparingly. Still, at 4-6 weeks, you'll need to start feeding again. Then I'd switch to an organic liquid food, and feed weakly weekly--a weak solution once a week, like 1/2 the strength suggested on the label.
Watering: Don't kill 'em with kindness. Tomato plants don't like to be wet all the time. They prefer to go just a little on the dry side (slightly moist), and then be watered well. Frequency will change over the season. Hot or cool temperatures, longer days, wind, sun exposure, your potting mix and the size of the plant all influence frequency. You may only need to water once a week in spring, and then once a day in summer when it's hot and the plant is larger. You'll need to get a feel for that. Don't be shy about sticking a finger down into the soil. Just because the top looks dry doesn't mean it's dry 6 or 8 inches down.
Staking: Most varieties need to be staked or caged, even in a pot. Unless you're growing a determinate variety or a specifically compact variety, don't bother with those crappy little wire cages. They are a waste of money and resources. One day you'll come out for a visit with your tomato friend and it will have pulled that thing out of the soil and be wearing it like a hat. Then it will fall over. You'll then have to figure out how to extract the plant from the cage without destroying both. Does it sound like I've been there before? Go to your local home improvement store and find the aisle with sacks of concrete. You'll see remesh mats--4' x 7' welded wire mesh sheets made for reinforcing concrete. Buy one. Roll it into a tube shape and wire it together so it will stay in the tube shape. Now you have a functioning tomato cage. Slip it over the plant, tuck it's arms and legs inside and secure the cage to the container with a long stake driven into the soil and wired to the cage. If you don't stake the cage down your tomato friend will one day yank it out and try to heave it across the yard. Continue to tuck it's arms and legs inside the cage as it grows.
A Note about Varieties: I think people assume that they must grow cherry varieties if growing in containers, but it's not the size of the fruit that matters as much as the growth habit of the plant. We offer a couple of cherry varieties that I swear would knock a 15 gallon container over, drag it around the yard and then become very unhappy. That said, I don't recommend most of the big, late season beefsteak varieties because the chances of getting only 2 or 3 tomatoes all season are just too high. If you're growing more than a couple of plants, the risk may be worth it. Many of the early and mid season varieties, and those that are prolific producers will do well for most people.
A Note on Drainage: Here's the part where I feed you more information than you wanted. One major problem with container growing is drainage. Even with a good potting mix you are likely to get water that just won't drain out of the pot, and it pools in the bottom making a soupy, airless layer that roots don't like. This is "perched" water. We all used to think that putting gravel or sand or pot shards in the bottom of our pots would eliminate perched water, but it turns out that physics doesn't work that way. I won't bore you with the details here (I'll bore you with it in another post), but gravel in the bottom of a pot only takes up space, and the perched water will still stick in the bottom layer of potting mix above the gravel. Now, sometimes plant roots will colonize that zone before it gets bad and use that water, but many times not. So what's the solution? Before you fill your container with soil, take a mop string, or absorbent length of rope and coil it around the bottom of the inside of the pot, then thread one end through the drainage hole and let it dangle a couple of inches below the bottom. Elevate the pot with pot feet or something that will keep the pot from sitting on the ground. Now fill your container with potting mix. The mop string/rope acts as a wick, drawing excess moisture down the string and out of the pot. It's the same idea as sticking the corner of a paper towel in a cup of water and watching the water get pulled into the paper towel. Are you asleep yet?
Wow, that was more like 10 cents worth of opinion. How about you? What works for you? Please share!