There are two basic ways to water your seedlings. Each have their own benefits, however we have our own preference, the second method "Watering from Below".
The first method is "water from above". Before your seedlings germinate, the easiest way to water is with a mister or very gentle spray bottle. Using a watering can disturbs a delicate seedling and it's easy to over-water.
When you water from above you are likely to knock over the fragile seedling even with a spray bottle. This is why it's best to start with a mister. It's also the cheapest. With a mist/spray bottle, you have to be willing to check on them at 2x a day to make sure they don't dry out. You'll also want to use a cover or humidity dome during this early germinating process to keep the moisture in.
Our preferred method of watering is from below. In our experience, it offers the most effective and reliable of the two options. Watering from below relies on capillary action (wicking of the water through the soil from the bottom working its way up to the top).
Bottom Water with 1020 Trays
With this method, you'll place your cell tray (or other growing pot with holes) in a flat tray. You can fill the flat propagation tray so that the water will cover about a quarter inch of the bottom of the cell tray when placed in the flat tray. Check daily. The main advantage of this method is how easy it is to get started, but make sure you check it each day. It's a good idea to use a cover or humidity dome for the first few days.
Bottom Water with Flood Table
Watering from below prevents any soil disturbance while watering, and this is best achieved with a flood and drain table. You also get the added benefit of not damaging the seedlings.
Regardless of the method you use, we recommend starting off with a medium that you pre-moisten. This will ensure your seedling is placed properly within the cell and has ample water to get started. You may also want to consider using a seed starter kit. These include a humidity dome that keep the moisture in similar to a greenhouse.