Find a place inside your home where you'd like to grow your garden. Preferably (and logically), this should be an area in your home that does not receive too much traffic.
Arrange a source of light. If your preferred area is in an east- or west-facing window, this is ideal. If, however, your home does not have windows where you'll be growing your garden (for instance, in a basement), you can use an artificial light source. Shop lights specific to indoor gardens can be purchased to provide light to your seedlings and plants.
Fill your containers (pots, bins, boxes) with potting soil, and arrange them in the area where you'll be growing your indoor vegetable garden. For best results, fill the containers outdoors, and wipe the dirt off the containers before taking them into the house.
Plant the seeds according to the directions on the package. Unless you keep your home unusually cold, there is no need to follow planting schedules. Just plant your seeds to the instructed depth, and cover the seeds loosely with potting soil.
Use a watering can to sprinkle water over the seeds. For the first several weeks, there is no need to saturate the entire container of soil. Simply water the top few inches, in order to get the seeds to germinate and grow.
Make sure that your seedlings receive 12 hours of light and 12 hours of darkness per day. If you use an artificial light source over your containers, position the light so that it's about 6 inches above the seeds. Once the seedlings sprout, raise the light source a little higher. Optimally, the light should be no higher than a foot above the seedlings, because this will result in thin "leggy" seedlings that will not be very strong.
Tend to your garden regularly, watering each container when it feels dry to the touch. Continue giving the plants regular doses of light and darkness, so that they will follow their natural cycles.
Use kitchen shears or gardening shears to harvest your vegetables once they start producing.