Tomatoes need a lot of sun, so build your raised bed in a sunny location. After you've constructed the sides, dig up the dirt at least 12" deep in the bed -- this isn't to give the roots room so much as to provide proper drainage. Just remove the sod (or toss it aside); if the ground is very hard, you may prefer to use a spading fork (figure A) rather than a shovel. When it's all dug up, add a mixture of topsoil, organic humus and cow manure to the bed. Now it's time to plant the tomatoes. I chose a variety called Goliath, which can grow to a height of 5 or 6 feet if not kept pinched back. Tomatoes can be planted deep, since the stems can form roots all the way along their length. Just open up the root system a bit and pop the plant into the ground. Don't worry about letting the plant lean (figure B) -- in a few days it will have straightened right up on its own. My raised bed is about 4 by 4, so it can comfortably sustain four plants (you can, if you like, plant some basil in the corners).
As tomato plants start growing, they will need to be staked for support. You can use wooden stakes, cages, or a form of wavy wire supports (figure C) around which you can train the plants as they grow.
It's essential that you water tomato plants regularly -- a condition known as blossom-end rot can develop when the soil is allowed to dry out. Be sure to keep the soil moist but not soggy, and feed the plants with vegetable food or 10-10-10. Also mulch the bed to hold down weeds and retain moisture, and in a few weeks you should have a grand crop of juicy tomatoes!