Many plants, such as tomatoes and peppers, have such a long growing season they can't be directly seeded into the garden in most northern climates. These vegetables are some of the most popular crops for a home gardener to grow, so northern residents have to push the season a bit. Start your seeds inside your home while the soil is still cold and damp, and by the time the ground is ready for planting you'll have healthy seedlings ready to transplant.
Research your vegetable varieties to find out the length of growing seasons. Most plant packages provide instructions on starting seeds indoors a certain number of weeks before your last frost date. You can find out this date from your local extension service or Farmers' Almanac. Plant each seed variety according to its correct start date.
Fill peat pots with fresh potting soil, leaving about 1/2 inch below the edge of the pots unfilled. This will leave room for water to pool in the pot before being soaked into the soil.
Plant two seeds in each pot, separating them about one-third of the way across the pot. Plant each seed at a different depth. Check your seed packet for these depths.
Water the peat pots until the soil is saturated. Place the pots on a tray and cover them loosely with plastic wrap. This keeps moisture from evaporating too quickly from the soil.
Place the trays in a sunny window when the seeds have sprouted and are poking above the surface of the soil. Make sure that the window gets at least six hours of sunlight each day. Remove the plastic wrap and discard it.
Water the seedlings whenever the soil surface dries out. Rotate tray at waterings so all plants can get a dose of stronger sunlight.
Clip off the weaker of the two seedlings when the plants have two sets of true leaves. Clip plants using small scissors or by nipping them off at the base with a fingernail. This allows the rest of the soil nutrient to be concentrated in the stronger seedling, giving you a larger plant when it's time to transplant to your garden.