Starting seeds indoors is a great way to get a jump on the growing season and always curbs my spring fever until I can get out in the garden. All you need to get started is some seeds, growing medium, containers and good lighting.
You can start seeds indoors using the light from a south facing window, but using cool-white florescent bulbs works best to keep the seedlings from getting leggy. You should keep the light within a few inches of the plants and move it up as the seedlings grow.
You can purchase plastic cell trays made especially for starting seeds or use what you have around the house, such as egg cartons or plastic containers. Just make sure they are clean and that you poke some holes in the bottom for drainage. If you are using containers from last years plants, it is best to clean them with bleach water to eliminate any possible diseases.
Use a good soil medium that is made for starting seeds to get them off to a good start. These mixes have a lot of peat moss in them, so it's best to mix it with water until you get it moist before you fill your containers. If you use the fiber pots, you will also want to wet those before filling with the soil mixture as they contain peat and will wick away the moisture from the soil.
Fill the containers to the top with the potting soil. Read the planting instructions on the package to determine the depth to plant your seeds and using your finger or pencil end make a hole to plant the seed, or just sow on top of the soil and lightly cover with potting mix, depending on the planting requirements.
Misting the plants is the best way to water so that you don't disturb the seeds. Keep them evenly moist. You don't want the soil mixture to get too wet or too dry. They can dry out quickly, so make sure to check the soil every day.
Once the first leaves emerge, you can give the plants a weak solution of fertilizer about once a week.
Before you plant your seedling outdoors, you will want to get them acclimated to the new environment, this is called hardening off. Place the plants in a protected area out of the sun where they will be cool and also protected from the wind. Placing straw bales around the group of plants is an ideal way to keep them protected and if it's going to get cold at night you will just have to place a covering over the top to prevent damage from frost.
After all danger of frost is passed you can transplant them to the garden. Use this handy frost map to determine the right time to transplant for your area.