Tomatoes need rich soil, a lot of water, and a lot of sun. Add compost to the soil before planting. Plant tomatoes 18-24" apart. 

Tomatoes need trellising. Here's some detailed info about tomato trellising options. As tomatoes grow, they also need to be trimmed. Prune off suckers on a regular basis (these are the shoots that sprout from the joint where the main stem and leaves meet).

Harvest time for tomatoes depends on the tomato variety, but they usually are ready to harvest when they're soft to the touch (but not too soft), full in color, and break off easily from the main stem. Harvest tomatoes by gripping the tomato's stem and snapping it off at the little elbow just above the tomato. You can also use clippers to cut the stem. 

Some people like to harvest tomatoes green and cook them, fry them, or pickle them. The varieties we're growing right now are generally best when fully ripe. 

Some tomatoes are determinate (all the fruit on one plant ripen at once) and others are indeterminate (fruit ripen over the course of weeks or months). It's important to know which type your tomato variety is!