I suppose everyone has their own ways, but for the way I do it...

First, I wouldn't use 'soil', instead 'seed starter', or germination mix is usually a better choice. Soil is too heavy for consistent results. Besides which, seed starter also contains ingredients with moisture retaining properties.

Next, moisten the medium prior to filling the trays/cells. The proper moisture is found with experience, but I like to use a spray bottle to overly moisten, let it soak up as much as it wants, then let it dry out (mixing/loosening it periodically) until it is a consistent wetness, but just beginning to dry. It will then be adequately moist, but also light and fluffy. Gently load it into the cells/trays to the top, then pick the tray up 3" - 4" and drop it on the work bench. That will firm it just enough. The level should drop down about 1/4", and the medium is ready to sow.

Sow your seed, then cover with more of the medium. Use a mister to moisten the surface slightly, and place your dome on top. Especially for peppers, place the tray on the heat mat (or warm surface) to keep the temp. of the medium at about 80 F. As soon as you see the sprouts breaking the surface, take it off the heat, and give it good lighting. Take the dome off if it seems too moist, and either fill the trays with 1/2" water (for bottom watering,) or use a mister to keep the surface moist. Try to find a balance for the moisture. Too dry, and the tender seedlings wither. Too wet, and fungi could cause them to die from damping off. A fan can help to control the humidity and moisture, and a mister is an easy, delicate way to keep the soil moist. The dome can help if you have to leave them for an extended time.

There are 'wicking' trays which allow for an even, and more controlled bottom watering, but without the wick and reservoir, you'll need to pay good attention to them at these stages. As soon as the seedlings form some 'true leaves' it's time to put them into a soil, or growing medium. At this point, they will need fertilizer of some sort.

I have this exact situation going in my kitchen right now. I used 9 cell modules with drain holes sitting in a tray with no drain holes. First I filled the modules with medium and filled the tray half full with water. The next day the mix was saturated and I tipped out any remaining water from the tray. On 19th Feb I sowed the seeds and topped the modules with cling film (saran wrap??). I use the top of my kitchen range/boiler for heat for the first week then just the kitchen counter. Since then I have not watered again. The cling film stops evaporation. 5 days ago the seedlings appeared and I removed the wrap and put the seed trays by the window. (I can hear the cries of horror that I don't use lights ;-) ) Yesterday I watered again, from below.

Horror! Horror!

Thanks guys!

Floral- You gotta get those seedlings under lights! ASAP! A window does not let in enough sun! Oh, I feel so sorry for your poor little seedlings. Stretching and contorting themselves in their futile quest to reach the insufficient light. :)

Sorry, couldn't resist. Anyway, back to the OP. How much you need to water is a question nobody can answer accurately. It depends on the potting medium you are using, the temperatures, the size of the flat or cells, how moist your mix was the first time, etc. Since you are using a dome you probably won't have to water until you take the dome off. I personally never use a dome (or plastic wrap as Floral does) and instead mist the top of the mix periodically with a sprayer until the seeds sprout, at which point I bottom water.

Rodney