Ginger is very easy to re-grow. Simply plant a spare piece of ginger rhizome (the thick knobbly bit you cook with) in potting soil with the newest (ie. smallest) buds facing upward. Ginger enjoys filtered, not direct, sunlight in a warm moist environment.
Before long it will start to grow new shoots and roots. Once the plant is established and you’re ready to harvest, pull up the whole plant, roots and all. Remove a piece of the rhizome, and re-plant it to repeat the process.
Ginger also makes a very attractive house-plant, so if you don’t use a lot of ginger in your cooking you can still enjoy the lovely plant between harvests.