Use moistened sterile seed-starting mix that is light and fluffy.
Use sterile containers with good drainage holes, and a shallow waterproof tray to hold the containers.
Locate the newly planted seeds in a warm place such as the top of a refrigerator, or radiator (prop few inches above, not on), or a heating mat. Loosely cover the containers with a plastic bag or plastic wrap to hold in humidity while the seeds germinate. The seeds do not need light at this stage.
Check the seeds daily. After the seeds sprout, remove the cover and move the sprouts to plenty of light to prevent legginess and weakness. Large sunny windows or under artificial lights are good locations. Temperature between 60 to 70 degrees in the room provide the best conditions for healthy plant growth.
Check the moisture of the soil. It should be moist but not soppy.
If you use grow lights, keep the lights just a few inches above the plants and move the lights up as the plants grow. If you grow plants on a windowsill, turn the plants every day so they do not bend toward the light.
Use a fan or other method to simulate natural breeze that helps to avoid fungus and white flies, and helps seedling stalks grow strong.
Move the seedlings outside after the last frost date. Place them in a protected area for a few hours on a nice spring day, a few more hours the next day, and so on, and bring them in at night. After a week or so, the seedlings will have acclimated to the outdoors and be ready to transplant.