Fresh mint is best stored at room temperature resting in a vase or glass filled with water with the stems attached. Fresh mint can also be frozen if keeping it fresh is not an option.
To store fresh mint in a glass of water, first trim the branches from the stalk. Remove any of the leaves near the bottom of the stem that is attached to the branch. Place the stems in a glass filled with a few inches of water, and place the glass in a sunny spot to keep the mint room temperature. Every few days, trim the stems again, and change the water to keep the mint fresh for longer.