Clear grass and other plants from the base of your tree. The more cleared earth you can afford the tree, the better the tree's chances for an adequate water supply. Obviously, you can't reasonably remove all the grass from under the canopy but clear a 24" ring around the base of the tree. Large trees will benefit from greater cleared space. Position sprinklers to water the earth around the tree (within the tree's drip-line) instead of the lawn. Water needs to be under the tree but not on trunk. Even twenty minutes of light watering every other day can make a difference for most trees. Freshly planted trees require a bit more water.
Fortunately, trees are tough and tend to be long-lived, which means they have excellent survivability. We're going to continue to lose trees during this drought but we're losing more than we must. Prioritizing your outdoor water-use may be the extra bit of help your favorite tree needs to get through dry times.
If you have any questions give us call; advice is always free and we're happy to help.