Let's look at the common causes for failure, and how to avoid them. First, people too often start their seedlings too early. This often means that the plants get leggy and weak. Yes, if you are just starting now, your tomato plants will be shorter than those you buy at the farm stand at the end of May, but they will catch up quickly once they get their toes in warm earth and bask in the hot June sun. You can minimize legginess by using supplemental lighting and growing them at the right temperature.
Adequate lighting is very important for any plant.
Many hardware stores sell inexpensive 4-foot long, two bulb fluorescent fixtures that will make your plants purr. Anything will do. The trick is to have your lights at the correct distance from the seedlings. This can be accomplished by suspending the lights from the ceiling over your plants. Place the lights about six inches above the plants, and as they grow, raise the lights as needed.