When shipping previously used bicycle wheels, clean them up first and get rid of any dirt or grease. Make sure that the wheels are completely dry before packing them.
Depending on the size of your tires, get an appropriately sized sturdy cardboard box that can snugly accommodate the bike wheels. You can get boxes from your local bike shop for a minimal fee or even free if you asked nicely. There are also commercially available wheel boxes which come in different sizes and can be used to ship single or multiple wheels. These boxes are specifically designed to hold bike wheels in place and keep them protected during transit.
Pack the box with sufficient packing materials to fill any empty space and prevent any movement. Use cardboard dividers to keep wheels from banging onto each other during transit.
Close and seal the box with heavy duty packaging tape. Address and label the package and take to your local post office or shipping company.