Decide when the plants go into the garden and count backward. Personally, I allow myself approximately 8 weeks.
You can start seeds in many different ways. My personal choice is to use the 72 cells with a solid plant tray underneath. I re-use my cells, trays, and domes each year until they break beyond use. I purchase these items from my local farm supply store in separate pieces. They are inexpensive this way vs. buying a kit.
Use actual "Seed Starter" soil; it is sanitized and formulated for this purpose. Moisten the soil in a bucket prior to filling the cells. It should hold together if you squeeze but not drip water. When I plant my seeds, I begin with the cells only about 1/2 full of seed starting mix. An old tablespoon works well for this; a dull pencil is great to poke the seed hole. Doing this helps delay the first transplanting (explained later). Cover them with either plastic wrap or a plastic dome. As they come up they will look really short in the trays.
These are placed on a 4' table in an east-facing window. This is also the entrance to the house so I do have to keep things a little orderly and neat.
This tray is shown after germination and about 1 1/2 weeks old. When the seedlings emerge, it is time to remove the plastic or plastic dome.
At this point I place them under florescent "shop" lights. Since I have yet to build a light stand, I simply prop my lights on top of some building blocks I have. Keep lights within inches of your plants, this will keep them from becoming "leggy." Regular florescent tubes work fine, you don't have to pay for "grow" lights.
Keep an eye on them and don't let them dry out. Watering from the bottom is best. This is why I invest in the solid plant trays. Water, wait 30 minutes, and pour off any remaining water in the tray - otherwise it is too much water and your plants may dampen off (rot).
Here you see the seedlings getting larger (top). Now, this is where I begin to fill in the cells as they are growing. Just a bit at a time. This will allow each seedling to develop a stronger/larger root system. You can see here that I have not yet thinned. I delay that for another week, to allow a little competition between the seedlings.
Here they are after another week. I am now thinning out each cell to the healthiest plant. I look at the size of the seeding, the leaves, and how strong the stem looks. CUT your seedling out with pointy scissors. Pulling disturbs the roots of the seedling left and sometimes pulls up your "keeper." I also take this opportunity to add a little more soil to each cell.
This is 1 week later...they really start growing now. Here, I did any final thinning of the smaller seedlings, again topped off any cells that still needed it. You can see especially with the tomato seedlings how thick their stem are getting. This day I also raised my lights (added another block).
You may read about having a fan blowing on your seedlings. This is to mimic the wind they will experience in the garden. Basically, the movement encourages the plants to strengthen their root and stem systems. A very gentle "jostle" of the leaves once or twice a day will have the same effect. It is kind of like "petting" your plants. If one or more of my boys are around when I do this - for their audience only... I add in a little "hello my little plants... you are getting so big...yes you are...." Yeah, totally unnecessary, but it has become part of our springtime routine.
In approximately another week, the tomatoes will need to be transplanted into larger containers. The peppers will continue to grow.