If you've never had a vegetable garden, here are some ideas to get you started.
Find a sunny windowsill where seedlings won't be disturbed and you can check on them daily. Or, you can set up some grow lights (pictured here using shop lights with full-spectrum fluorescent lights installed).
Before you go out and buy seeds, plan where your garden will be and how big it will be. Keep in mind, once summertime heat kicks in, you'll be out there tending to the weeds that inevitably grow several inches overnight! Carefully read the planting instructions for the vegetables that you decide to grow. Some do well in short, hot summers (like we have here in Denver). Others do well in cooler, more temperate weather. Some vegies really need to be started indoors due to their longer maturity time (like tomatoes, peppers and some herbs). Other vegies like to be planted directly into warm soil outdoors (like squash, pumpkins, cucumbers, carrots, radishes), while others need to be planted before the temp gets too warm (like peas and lettuce).
Last year I tried to plant my sweet peas around St. Patrick's Day, even though, here in the 'burbs of Denver, we are hardly out of the winter season by that time. It was the first time I tried something so daring. I even threw out a few lettuce seeds, just to see what would happen. Lo and behold! They sprouted and I actually my first decent crop of sweet peas since I began gardening in the harsh climate of Denver.
Soon I'll be getting out my shop lights and setting up the grow area in the patio room. Last year was the first year I tried this set-up. Our patio room isn't insulated and the temps can drop to freezing or below until around Mother's Day. Nevertheless, the patio room was temperate enough to keep my young seedlings from freezing. It probably helped that I had a warming mat, designed especially for starting seedlings, under one of the trays with tomato seeds, and the grow lights provide some warmth. I had the lights on a timer, so they go off at night to give the seedlings some rest, but I kept the mat on 24/7. It was only under one of about twelve trays, so it was only a slight help.
Once the soil warms and the danger of frost is past, the kids help me plant a sunflower house. Here are some pictures chronicling the growth of our house a couple years ago. I was afraid we'd started the house too late, since we started in on Memorial Day weekend, and it seemed to grow very slowly in the beginning. After about 6 weeks it looked like this:
About two weeks later it looked like this:
And by late summer, we could go inside our sunflower house and find a cool retreat from the day, like this: