Volumes have been written about the intricacies of tomato culture, and no very comprehensive analysis can be offered here. But there's no need to mystify what can essentially be a simple process of allowing the plants to do well what they want to do anyway--supply the gardener with an abundance of sweet, delicious, juicy fruits, which after all are nothing more than the distilled essence of summer sunshine.
There's nothing unique about tomato culture--the plants want full sun, fairly hot days and warmish nights (above 50 degrees Farenheit). They grow best in rich soil, generously amended with good compost, and preferably well mulched to conserve soil moisture and stabilize soil temperatures. After a proper hardening-off period, set your plants in their final positions after all danger of frost. (Or set them earlier, but be prepared to protect the plants against the final frosts of the end of spring. Utilize wall-o-water devices, or find some way to cover the plants on those last chilly nights.)
The plants need ample soil moisture, but not standing water for any great length of time. Excessive variations in soil moisture are known to produce "cracking," which occurs when the fruits swell so quickly that the skin cannot accomodate their growth. Some heirlooms are prone to this anyway, while others are more resistant, but even moisture is the best defense. Don't let the soil get too dry, then attempt to compensate by watering agressively. Instead, use mulch, poke your finger into the ground occasionally, and try to maintain a fairly constant level of moisture. Cracked fruits are fine to eat, but not so attractive, and certainly won't keep as well. Use them in cooking, and save the more perfect fruits for fresh use.
As the plants grow, they unquestionably require staking. If staking is omitted, the plants do fine, but sprawl untidily on the ground. The fruit will be harder to pick, and is apt to rot in contact with the soil, although here again, a mulch can be helpful. There's no great art to staking; the objective is merely to support the plant, keep fruits off the ground, and prevent branches drooping or breaking under the weight of the crop. Tomato cages are ubiquitous and certainly easy to use, but a great many heirloom types really get too big for them, eventually hanging over the tops and possibly breaking under the unnatural strain. A better, but more time-consuming method, is to drive stout stakes into the ground, and simply tie branches to them as they begin to show their need for some support. Metal T-posts, or one-inch-square oak stakes are re-usable, and work extremely well. Do try not to crowd the leaves too closely together as you tie; leaves absorb the sun's energy and transform it into the sugars that enable the fruits to develop. They can't do their job if they're closely bunched together in each other's shade!
With some heirloom types, it is hard to judge just when the fruit is ripe until some experience has been acquired with the variety grown. Early in our heirloom-growing career, we once waited all summer for pink fruits with green shoulders to turn red--they never did! Most varieties turn soft when ripe; indeed this attribute is one that makes many of the the old-fashioned types so desirable for the home garden. They are just too soft and delicate to ship well. And don't be afraid to learn by trial and error--if you pick too soon, you'll know better next time. And even half-ripe, the fruit is bound to taste better than the crunchy, tasteless facsimile tomatoes available at the mainstream grocery!
Occasionally, the blossom end of the fruit turns black and dries out, causing the remainder of the affected fruit to ripen prematurely, and usually very small. The malady is called blossom-end rot, and some authorities swear it's caused by a calcium-deficient soil, while others feel it's due to excessive watering. Fortunately it usually affects only a few of the earliest fruits. Just remove them, and consider adding a calcium-rich soil amendment in next year's tomato bed. (An organic source of calcium is bone meal, but we doubt that an after-the-fact application can work through the soil micro-ecosystem fast enough to do this year's plants much good.)
Another common problem is the tomato hornworm, which can reach four inches long, and can defoliate a plant in a few days. If yesterday's lush foliage suddenly becomes today's leafless stumps, look for the hornworm. Hand-picking is effective, but the critters hang on until you're afraid they'll pop rather than let go. But they must be removed or the plants will suffer terribly.
When summer turns to fall, pick your last tomatoes before frost takes them. They'll ripen indoors. Some varieties can actually be stored for many weeks in the green stage (at cool room-temperature, perhaps wrapped in paper), and subsequently brought into the warmth of the winter kitchen and exposed to indirect light. True, they won't taste like the ones you had in summer, but they'll certainly be better than the ones you can buy at that time of year; and they'll provide a nostalgic reminder of summer past, and summer yet to come.
Enjoy growing your heirloom tomatoes!