Cut off the growths with about an inch of the potato, and plant it in the garden. Sometimes you can cut a potato in about half a dozen pieces, each with a shoot on, and plant each of them. Each piece will grow into a potato plant, yes, really, each one a new plant. Each plant will produce a crop of potatoes.
Admittedly, the crop will not be as large as from a seed potato, but then it's cost you nothing but a little time and effort. The magic of nature works for you - aren't you lucky?
That's what I did about 3 weeks ago, and look at the growth they've put on!! To obtain a larger yield of potatoes, simply pile earth up against the stems of each plant. The obliging potato will generate new roots into this fresh soil, and they will produce the tubors for you. Even better magic, and more free food :-)