I realize that writing about how to water trees while we've been having many rainy days is not the best timing. You just have to look at North Eastern Ontario to see that weather can change quickly and within a week or so, we may be hit by drought and hot temperatures just as easily as more rain.
Here's a short assignment: before reading any further, take a second to think about where you think the roots of a big tree may be. The answers of "in my sewer pipe" or "pushing up my asphalt driveway" may be true but that's a whole other issue. How deep are tree roots? How far do they spread away from the trunk? How large or dense are they?
First let's dispel some misconceptions. Large trees do not have tap roots and their roots don't go several feet straight down through the soil to find the water table. They also don't magically stop growing at the dripline.
Tree roots are surprisingly shallow. They prefer to grow in the top one foot of soil, their small feeder roots intermingle with grass roots right at the soil surface. They extend very far from the trunk of a tree and although there is no firm rule for their spread, the length of their extension can be double or more the distance of the trunk to the dripline.
The roots right at the trunk, what we call the root flare or the root plate, function only to support the tree (very important!) and to conduct water and nutrients to and from the outer feeder roots. These structural roots don't absorb water and this is important to understand. You never want to douse this part of a tree with water because it won't get moisture into the plant, it will just lead to potential root decay problems.
To provide hydration to a tree, you want to target your watering on the absorptive roots that lie towards the dripline of a tree and beyond. Although some may recommend the "slow drip" method of watering, I'm too impatient for that. Common sprinklers work great as long as you are not applying so much water that it runs off the surface of the soil. A long watering of 1 to 2 hours will ensure that water gets through the grass roots and permeates through the important top one or even two feet of soil.
Make sure the sprinkler that you uses doesn't get the tree leaves wet, this can exacerbate leaf disease problems. Water low, water wide and cover the entire rooting zone of a tree inside and outside of its dripline.
For newly planted trees, you can water close to the base of the tree only for the first year after planting. The second growing season and beyond, watering should be focused well outside the planting hole to encourage roots to spread and grow away from the trunk to avoid root girdling problems.
As always, for the best advice on trees and their needs, consult a certified arborist.