Each seed is started in one gallon fabric grow bags (e.g. Smart Pots) filled with a sterilized potting mix specifically designed for seed germination (Miracle Gro Seed Starting Mix, Fox Farm Light Warrior, etc). Once the containers are filled to the top I gently water until I see run off. At this point they usually sink down a bit, so I'll refill with more potting mix and water, then I place them to the side to drain for a few minutes.
While this is going on, I take my seeds and soak them for 5 minutes. Some will float, some will sink, all will be sowed. Once the soaking is done, I place them on a paper towel and dust them with mycorrhizae inoculant (only if they'll be transplanted outside into the garden). Once dusted they are ready to sow.
To sow them, I use a pen or pencil to poke a hole that's roughly 1/2" deep. I drop the seed, then pinch the hole closed. Followed by a quick and light misting.
I immediately place them under my lights (in photo above I'm using a single 200W 5600K CFL with a Hydrofarm Hood which has been raised to take the picture), which I leave on for 24 hours straight until they pop, lightly misting as needed, but just enough to wet the first 1/2" of potting soil.
Once the seedlings pop, I set my light's timer to 18hr on and 6hrs off and stop misting. From this point on I only water when the container feels 50% lighter. After the third week from sprouting, I'll begin the hardening off process and by the fourth week they are transplanted outside into the garden.
I love this method. I never lose a seed because of rot, my stems never come out lanky or starving for light, and my roots establish themselves much faster then if they were per-germinated and transplanted (e.g. paper towel method). I also avoid domes or raising humidity because in my experience, more often then not it creates mold.