I start with packaged potting mix and seed starting mix. Any brand of potting mix will do, but I really prefer Jiffy seed starting mix over all other seed starting mixes. You might wonder why I need potting AND seed starting mix. It's because I'm cheap. Seed starting mix is fine-ground stuff, and because it has to be ground up more, it's costlier. I use potting mix on the bottom of each pot and seed mix on the top, where the seeds are. Duh.
The most common container I use are these 4-cell plastic ones. I like them because they aren't too small, so I don't have to transplant to larger containers later on. I've had huge success using them for tomatoes, from germination to direct planting into the garden. However, anything that will hold mix and allows water to drain out will work. My second favorite container are actually toilet paper rolls. Packed tight in a large container (with drainage holes), they are fantastic...free, allow for lots of root growth, and can go in the ground with the plant for minimal trauma.
I moisten my mix in the bag. I slice open the top of the bag, and pour 2-3 pitchers of water in. Let it sit overnight, and in the morning you've got nice wet mix. Pouring dry mix into cells and then trying to get it moist sucks. Save time and pre-wet your stuff. I fill the cell 2/3 with regular potting soil, and the upper 1/3 with seed starting mix.I make some holes in the top of the seed mix. Not deep, just a little depression to catch seed.
At this point, I tear off a rectangle of clear plastic wrap and put the filled pot on it. No name brand wraps either. Only the cheap store brand stuff will do.
Even though I'm using moist mix, I add a splash of water to each cell at this point. I want this stuff dripping wet. No water, no germination, no seedling.
I add a little sign so I have a clue about what this it later when there are 500 plants growing in the greenhouse.
Then I wrap it up and put it in a sunny place in the greenhouse. Once I see green through the plastic, I unwrap it. However, until then, the plastic guarantees that the mix will be at the perfect moisture level for germination. All you need now is sun and warmth. The rest is up to the seeds.