In some cases, a hard spray of water to physically knock the aphids off the tree will do the trick. If you have a hose with a spray handle that can reach the affected tree, this can be the most cost-effective method to try first before upping the ante.
Consider applying an insecticide to the tree and the surrounding area to treat the aphids. Because the life cycle of aphids is so short, you should look for an insecticide which provides a residual effect against the aphids. Different varieties you could try include permethrin, acephate, beta-cyfluthrin and estenvalerate.
Apply natural predators if you'd rather use an organic, long-term option, or have other reasons (such as a pet in the yard) to shy away from insecticides. Many garden supply stores may be able to supply natural predators to aphids, such as lady bugs, damsel bugs and lacewings.