Wow. Lots of different approaches here.
I break up most of my "seed starter trays" to 6-packs before starting. Then, I fill the cells with potting mix or "seed starting mix" to 1/4 or 1/2 inch below the top (the "planting depth" for whatever I'm planting). I set those in a tray of water to "bottom water" the mix to near saturation. Then I let the outside of the packs dry, so I can put my masking tape markings on the things. I always mark before I even put the seeds in, so i don't forget. I use my finger to gently pack things a bit and place a couple seeds in each cell. I cover the seeds with seed starting mix to fill the cell (which should be the correct "planting depth") and I use a spray bottle to mist the top mix to get it moist.
This year, I've been "watering" my seed trays with the spray bottle, and I seem to not have as much problems with overwatering. I'm sure I'll figure out how to overwater, even with the spray bottle. I used to use a small watering can with a very small tubular spout (less than an eighth of an inch opening), and that was pretty good for me, but the spray bottle method is working even better.