The timing for when to start vegetable seeds varies by cold hardiness zone and last frost date. Minnesota's cold hardiness zones range from zone 4 in the southernmost areas of the state, and down to zone 2 in the most northern parts. Your best seed start times are determined by your zone and local climate, so be sure to check with the local agricultural extension office or with local plant nurseries. See the Resources section for a detailed hardiness zone map.
Pick the right starting medium for the type of vegetable seeds you want to start indoors. A balanced vegetable potting soil works for many kinds, but may be too dense for some delicate seeds. You also can find special soil for cucumber-type vegetables or tomatoes at garden stores.
Amend the medium as needed. It's usually a good idea to loosen it up with the addition of sand, perlite, vermiculite, or peat moss. Mix it well before putting it into seed trays. This helps air and moisture circulate around the new seeds. If you are reusing old seed trays or pots, clean them well with a bleach mixture to be sure no old germs or pests are transferred.
Choose your seed starting time. You can start vegetable seeds as early as March indoors in a sufficiently warm and lighted location. They should not be transplanted outside until after the last frost date in your area, which can be as late as June in northern areas. Consider the harvest time when planting; vegetables with a short production time may not need to be started indoors at all. See the Resources section for a list of germination and harvest times.
Plan a location for the seed trays. They should have light for 12 to 14 hours each day; this will likely mean suspending fluorescent lights above the trays. Full, direct light is needed, so before sprouts show, 6-8 inches away from the trays is ideal. Once sprouts show, the lights can be raised so the tender shoots don't burn.
Plant the seeds in the trays. Put two or three seeds in one hole. Don't bury them too deeply; most vegetable seeds do well about a 1/2 inch to 1 inch down. Check directions on the seed packet, since some seeds should not be covered at all. Add fertilizer, but not right next to the seed as it can burn the seed. Instead, tuck it elsewhere close by. Add some water to the trays when you are done planting, using a watering can or mister so you don't wash seeds away.
Keep trays in a sunny location when possible to generate the amount of heat needed for germination. Water daily, or as often as needed to keep soil dark and not dried out. Most vegetables sprout within 2-3 weeks. Pinch off the weaker sprouts in each group of two or three if they all come up.
In cold climates like Minnesota's, a hardening-off period is needed before transplanting seedlings outside. When the sprouts are a few inches tall and growing strongly, place them outside for a few hours a day, gradually lengthening their time outside until they are out all day and only brought in at night. Once the last frost is past in the spring, they can be transplanted to your garden.