During the growing season, your rooted cutting will have formed a tuber. A firm, potato-like storage organ that will provide your dahlia with everything it needs to be able to survive, dormant over the winter and grow again the following spring.
The big question is 'to lift' or 'not to lift', there is no simple answer.
In general growers lose dahlias overwinter because they get wet and drown rather than because of the cold so in general we would suggest lifting in the autumn if your garden is a clay soil type or otherwise becomes waterlogged.
Cut plants down after the first hard frosts, lift carefully, turn upside down and store somewhere dry. You may wish to dust the stems with 'Flowers of Sulphur'.
When the soil surrounding the tuber has dried, carefully ease it away and store the tuber in an open top box (not cardboard), in just damp peat or spent compost.
Store the box in a cool but frost free location.
In the spring you can put your tuber in a pot, under protection and you may also at this time consider taking cuttings.
If you decide to leave your tubers in the ground over winter, cut them down and mark with a stake, then cover with 3 or 4 inches (7.5cm to 10cm) of mulch- garden compost, spent mushroom compost, or straw are good options.
In the spring keep an eye out for slugs early in the season and use your preferred slug prevention strategy, as slugs love the young shoots even when under ground.