For each of the last 15 years, I've grown between 50 and 100 tomato plants from seed, which gives me a year's supply of tomatoes, tomato juice, tomato sauce, and salsa. And plenty to give away, also!
In southeastern Kentucky, the "frost safe" date is May 10th. To grow tomatoes from seed, you should start them 6-12 weeks earlier than your local frost safe date. I remember to get started sometimes between the Super Bowl and the SEC basketball tournament.
Start your seeds in a very light soil medium, either a commercial starting mix or a homemade mixture of sphagnum moss and vermiculite. I add some anti-fungal agent to prevent mold. Mix it with just as much warm water as the soil will hold. I plant the seeds in leftover food containers, label the variety (there are four different kinds this year) and cover the tray with a loose baggie. Then place the trays in a warm area, like on top of the refrigerator. When they sprout, remove the plastic and place them in a window or under a plant light. Water when needed, then drain the excess.
I built special shelves in my southern-facing windows for plants. Young tomatoes need as many hours of sunlight as you can give them. Some of these plants are peppers and marigolds.
When the seedlings have four leaves, you can separate them into their own pots. I use 2- or 3-ounce plastic bathroom cups, with holes in the bottom made with an ice pick. Peat pots dry out too quickly. Use potting soil, or a homemade mix of topsoil and your seed-starting mix. If you use compost, make sure you're not bringing insects into the house. Carefully jiggle the roots apart. Handle the seedlings by the leaves, not the stems, and try to preserve the roots. Bury them up to their necks, so that more roots will sprout from the underground part of the stem.
If you plant more than one variety, label each cup, or else you'll never know how many you have of each when planting time comes! The CHE here is to designate cherry tomatoes. Water them thoroughly immediately after potting and check the pots for drainage.
There is never enough window space, so I have a couple of plant lights as well. They run 24 hours a day so I can rotate plant trays under them for 12 hours at a time.
When the outside temperature is above 50 degrees, you can set plants outside in the sun. This can be a chore, carrying plants out in the morning and in at night, but eventually the weather will be warm enough to leave them out overnight. By the first of May, I figure out how many plants of each variety I will need. I sell the others, which pays for my planting supplies, and give quite a few away to family and friends.
Get your garden plot ready before the frost safe date by tilling the soil, laying a plastic mulch (if you don't like to weed), and setting up a trellis. A trellis will keep the vines and fruit off the ground. I use whatever is available, of course, so this trellis is made of branches, broom sticks, pipes, and rebar. Tomatoes should be planted two feet apart in rows three feet apart. That seems like a lot of room, but you'll need every bit of it. Unless you kill the plants.
A wise man once told me you should dig a ten-dollar hole for a one-dollar plant. I dig a deep wide hole for each tiny plant and fill the hole with compost. Then I push the plant out of its pot by pressing on the bottom and slip the plant into the compost, once again burying it up to its neck. You can use the pots again next year. Water thoroughly soon after you plant. Wipe your feet before you go inside.
Water your plants every week if you don't get a good soaking rain. It's astonishing how fast they grow once they're outside! Use some soft string and tie the vines loosely to the trellis as they grow. You can see yellow tomato blossoms in this picture if you look closely. A pint of liquid fertilizer per plant every week will do a world of good at this stage, especially if your soil isn't all that great. I mix up 15-20 gallons of fertilizer at a time for this garden.
Before long, the vines will be huge and you'll see some green fruits. Since they are green, you won't see how very many there are. I don't need to use pesticides, but you should keep an eye out for symptoms, especially if you use heirloom seeds. Modern varieties are quite resistant to disease and pests. The border of marigolds keeps out nematodes. The only critters that are drawn to my tomatoes are turtles, which can be apprehended and redirected easily.
Eventually, you'll spy a tomato turning red. This is a glorious day in the garden! It happens in mid-July where I live; your mileage may vary. For the rest of the month, I have enough tomatoes for salads and sandwiches. Then in August, I have to take a five-gallon bucket out twice a day to relieve the straining plants of their burden. Grocery stores love to advertise "vine-ripened" tomatoes, but I finish ripening most of mine in a window. Otherwise, the weight would tear the plants down! I pick tomatoes that are orange or light red. Once they start to turn color, they won't grow any bigger. When they are all red, they are the most delicious thing you've ever eaten.
Through the month of August, I am up to my elbows in tomatoes. The ripest are in the refrigerator, the barely ripe are on the counter, and the ripening fruits are in the window. When a bushel or so are ripe enough at the same time, I peel, chop, cook, and can them. By the time I come up for air in September, I have a year's supply of tomato products, a kitchen spattered in tomato juice, and a garden that has settled down to producing just enough for salads and sandwiches until the end of October.