Choose which vegetables you'd like to grow from seed. If you don't have the room or resources to start seeds indoors, many vegetables, such as radishes, carrots, beans or peas may be sown directly into the garden. Other vegetables, such as tomatoes, melons or squash are better started indoors, especially if your growing season is short. Note the days to maturity for each vegetable, and apply this to your local growing season. For example, if a certain variety of pumpkin is 120 days to maturity, and your growing season is 100 days long, you'll want to start those seeds indoors at least 20 days before the predicted frost-free date for your region, factoring in an extra week or two as insurance.
Prepare seed trays or other containers for any seeds started indoors. Purchase seed starting trays at any garden center, or reuse items from around your house, such as egg cartons, yogurt or cottage cheese containers or the bottoms of milk cartons. Do not reuse containers that once contained potentially toxic substances, like cleaners or chemicals, and rinse any reused containers thoroughly before proceeding. If you reuse plastic seed trays from previous years, wipe them down with a highly diluted bleach solution (1 part bleach to 9 parts water) and rinse very well. Doing so will kill off bacteria or viruses that may have harmed your seedlings last year. If your container does not have any drainage holes, poke a few holes in the bottom with a nail.
Fill the seed trays or containers with potting soil or another growing medium designed for starting seeds, available at most garden centers. You may want to moisten the soil or growing medium before filling the containers to avoid disturbing the seeds by watering them later.
Plant your seeds. Most seeds do not need to be sown very deeply, and are best if they are just barely covered with soil. Refer to the seed packets for specific instructions for each vegetable. Plant two seeds together every 2 inches.
Label each tray or container with the variety of vegetable and the date planted. Save the seed packets for future reference.
Water the seeds (if you did not moisten the soil ahead of time) and cover the trays with clear lids, or place the containers in an open, clear plastic bag. This will help retain heat and maintain moisture levels. You may want to poke a few pinholes in the bag for air circulation.
Place the seed trays near a south-facing window or under a strong light. You do not need to purchase special "grow lights" at the garden center---any bright fluorescent bulb will do---but a grow light may be easier to position than your average desk lamp.
Check the seeds daily to make sure the soil doesn't dry out. The soil should always be damp to the touch. Water the trays with a fine mist bottle to avoid disturbing the seeds.
Remove the lid or plastic bag as soon as sprouts emerge. Thin the seedlings to 1 every 2 inches, and continue watering as needed.
Transplant your sprouts outside after the danger of frost has passed. Harden off your seedlings by placing them outside a few hours every day until they become acclimated to the outside temperature.
Direct-sow the seeds of fast-growing or cold-season crops like radishes or beans. Prepare the garden bed. Bury the seeds to the recommended depth and density, then water gently. Weed as necessary, and remove weak or sickly plants so that the healthy plants will have room to grow and spread out.