Use a rake to rake away any fallen acorns in your yard. This will clean away any acorns that haven't taken strong root into the soil yet. Place the raked acorns into a waste bag for disposal.
Pull up any larger acorn trees by hand by taking hold of them by the base, as near to the soil as possible. Lift up to unearth the acorn trees and dispose of them in waste bags.
Purchase a broad-leaf herbicide, which can be found at most home service centers. Prepare the herbicide, if not already prepared, according to the manufacturer's instructions.
Spray the area inhabited by the acorn trees with the broad-leaf herbicide. Refer to the herbicide product label for specific application instructions. The leaves of the oak trees should absorb the herbicide and carry the poison to the roots, killing off the plants.
Inspect the sprayed area frequently for signs of new growth. Repeat the herbicide spray application as needed to keep the area free of acorn trees.