Trees are notoriously slow growers. Even varieties of trees that are known for their "quick growth" take years to reach their mature heights. While you can't make your tree spring up to full size overnight, there are a few things you can do to ensure it is growing as quickly as possible, so you can enjoy its lush shade and towering stature sooner.
Mulch around the base of the tree.
One very simple way to increase tree growth is to place a thick layer of wood mulch around the base of the tree. The mulch will serve two purposes. First, it will seal in moisture during drier periods, so your tree has access to more water (and more water leads to more growth). Second, the mulch will slowly break down, acting as a fertilizer to add organic matter back to the soil for the tree to use.
Choose an organic wood mulch -- preferably one that is free from dyes -- and spread it in a circle with a 4 - 5 foot radius. You want a layer that's about 4 inches deep. Do not push the mulch all of the way up to the trunk, as this can trap in moisture and lead to rotting. Add an additional inch or two of mulch two or three times per year to replace the mulch that breaks down. You can find wood mulch at a company like The Bushel Stop.
Water at the root level.
Many people water their trees incorrectly, which may inhibit their growth. Instead of watering your tree from overhead by spraying it with the hose, you should be watering the ground around the tree. When you water from overhead, you expose the leaves to moisture, which leaves them susceptible to fungal infections. Even if your tree does not become fully infected (and often, it won't), it has to expend energy to defend itself against the fungi that try to take up residence on its moist leaves. This is energy it could otherwise be using to grow.
Water your tree at the root level by simply placing a hose a few feet from its base and letting it saturate the ground. After 10 or 15 minutes, move the hose to the other side of the tree, so the ground on both sides gets equally wet and a greater portion of the roots get saturated with water.
Watering your young tree is a good idea during periods of drought. Just because your young tree may survive a drought without additional water does not mean it's experiencing maximum growth during this period.
By mulching around your tree and remembering to water the soil, not from overhead, you'll encourage your tree to grow more quickly and more healthfully.