Answer: If it is a very large shrub, it will be nearly impossible to dig it up and move the whole thing. Instead, you might try digging a sucker and potting that up. If it is a relatively small shrub, you can try to move the whole plant. Wait until the plant enters winter dormancy before digging. Be sure to keep the rootball intact as much as possible, and retain as much soil around the roots as you can. Pot it up in a large container and water it well. (Note that even a small shrub will have a relatively large rootball, and that this will be quite heavy to lug around.)
Whether you've potted up a sucker or removed the whole shrub, you will need to protect the plant from extreme temperatures over the winter, but also keep the shrub in a cool enough location so it stays dormant during the winter. You might be able to achieve this by keeping the pot in an unheated garage or other sheltered location that stays reliably cool.
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