Once each plant has been thoroughly watered with a slow trickle running at the base, the best way to regularly check the moisture level is to stick a finger down past the mulch a couple of inches just like you would check a houseplant for moisture.
If the soil is moist at that level, the soil below it will likely be moist. If it is dry, then do a slow trickle again around the entire root ball. If you have a sturdy stick or metal rod, it doesn't hurt from time to time to stick that down in beside the root ball to check the moisture level.
While you don't want the plant to go dry, you also don't want it to stand in water! Remember, roots need oxygen. They can't develop if they are constantly saturated so, it is important to allow the porous space of the soil to dry out inbetween waterings.
A good general rule of thumb is to water your Arbrorvitaes like you should your lawn - fewer longer soakings rather than numerous light showers. This will promote good root growth.
As for staking - only do so if the trunk appears loose in the root ball. You don't want much movement but you do want some stress (from wind) on the plant so that it develops a strong stem. Staking when unnecessary can result in a weakend stem so, do so as necessary but use caution not to leave it on any longer than necessary (once the roots have established beyond the root ball).