When you start your vegetable garden indoors from seed, the first leaves you see aren't actually leaves. They are a food source for the seedling.
True leaves will come next, and when they do, it is your cue to start fertilizing the seedlings once a week with a half dose for three or four weeks. (It is best to use an organic fertilizer. And seaweed- and kelp-based fertilizers seem to have a wonderful effect on seedlings.)
During this time, your seedlings will need a lot of attention: Water them regularly and evenly, but don't allow the germination mix to get soggy. The humidity underneath the plastic wrap or plastic dome has to be just right -- and there needs to be air circulation -- or mildews and molds and fungus will develop. You might need a small fan.
You will want to transplant your seedlings into larger pots, with a mix of potting soil and perhaps a little garden soil, when they have three or four sets of leaves. Don't wait too long, or you might damage the seedling in the process.
Peat pots or CowPots or newspaper pots are ideal for the transplanted seedling because you plant the whole business in the garden when it is time, protecting the delicate roots.
Two or three weeks before it is time to transplant the seedlings to the garden, expose them to the sun, wind and cold of the outdoors a little more each day.
When it is time to put your plants in the garden, choose a mild and overcast day with little wind. You might consider one more pampering move: a row cover to protect these tender plants for a few more weeks.
Above all, rely on the advice and directions on the seed packets. They are the best source of information for starting your vegetable garden from seed.