Traditionally, a lot of home gardeners wait until spring is established, then go to a garden center and purchase growing seedlings and plants for their garden. This generally results in a limited variety of plants for the garden. Peruse seed catalogs and you can find dozens of varieties of every plant you want to grow. Growing seeds is not much more difficult than growing plants and takes very little extra time for a much greater payoff.
Study your vegetable types to determine which should be started inside before outdoor planting and which can be directly seeded into your garden. Your seed catalog or the back of the seed packets will give you this information.
Start seeds indoors that need a head start and that will be planted outside as seedlings. Fill plant pots with soilless planting mix. Plant two seeds per pot. Place seeds in a tray, water thoroughly and cover. When seedlings sprout, remove the cover and move the tray to a sunny window. Water frequently so that the seedlings don't dry out. When the seedlings are about 2 inches tall, clip off the weaker one to allow the stronger one to grow better. Ruffle the seedlings once a day with your hand, or allow a breeze from the window to blow on them, to help them to grow stronger.
Plant seeds directly into the ground with varieties that do not need transplanting, after all chance of frost has passed. Turn over the soil in your garden, removing any rocks and roots. Mix in compost with the top 6 inches of soil. Smooth the soil with a rake. Plant seeds in rows or blocks, according to the package directions, and water thoroughly.
Plant seedlings after all chance of frost has passed in soil that has been prepared as above. Make sure that the plants have room to grow, planting seedlings according to the seed package directions. If there is any chance of frost overnight, cover seedlings with black plastic at night and remove it in the morning.