I'm not really a soil guy but...I saw a quote around here that when watering seedlings it shouldn't be called watering, it should be called dampening. If you aren't doing the coffee filter or paper towel method (which is what about 95% of people do, myself included) keep the soil moist don't let it dry out. You might even want to put plastic wrap over the pots to prevent drying. Once they sprout you don't want them to dampen off which happens with soggy soil, you might be better off misting the top of the soil with a spray bottle to keep it damp not drenched.
For air circulation I wait till they have formed there first true leaves then turn on a fan in my veg/clone/seedling cab. You don't want the fan blowing directly on seedlings but moving enough air in their space so the babies are gently moving. This will help prevent mildew at this stage and strengthen the stalks. Later in bloom you will want fans blowing directly on the plants to prevent mold/bud rot.
Hope this helps, I'm sure some more experienced soil/soilless growers can more thorough advice.
Edit I should probably refresh the browser before I reply after topping off my coffee