Trees absorbing moisture through the roots supply leaves with water using a decrease in water pressure in the leaves. This pressure difference "siphons" the water from ground to leaves and is necessary for a tree to survive. Ninety percent of tree water is eventually lost into the atmosphere through evaporation. This beneficial loss of water from plants is called transpiration.
Young seedlings planted this season should be your main concern. You need to remember that trees can suffer from drought in winter as well as summer. Recently planted trees need extra attention since they are still trying to replace roots lost in the transplanting process. But all moisture sensitive trees need watering during dry periods.
The National Arboretum suggests that "In areas where water is available, you can most effectively water trees by turning the hose on to a trickle and placing it a few feet away from the trunk. Let it trickle for several hours to moisten the soil in the vicinity of the tree thoroughly. One to four hours time may need to pass to accomplish this as well as loosening any hardened mulch that resists water."
"Plunge a trowel or spade into the earth to check to see if the soil has been moistened to a depth of at least six inches. If you run into dry earth, more water will be needed. Once watered, you may not need to return to water the tree for two or three weeks."
If you are limited to hand watering, build a small circular "berm" of soil a few inches in height a few feet away from the trunk. Fill the basin you have created with water. it will then seep into the soil slowly. If your soil is heavy, you may need to fill the basin several times over a period of several hours to get the soil moistened to a depth of more than six inches.
Always mulch but not excessively. Over mulching can be repellent to water so mulching correctly is very important