Some fuchsia varieties, such as 'Genii', are hardy and don't need any special treatment overwinter. But most varieties are half-hardy and would be killed by the frost if left outdoors all winter. When Which? Gardening magazine trialled different ways of overwintering fuchsias we found that the following worked best:

Caption: Tender variety 'Walz Jubelteen'

Lifting and potting fuchsia plants

The plants we lifted and potted up to be grown on in a warm greenhouse fared best. This method can make plants die back and we had to remove some dead branches. The plants from one of our test sites had slightly paler leaves than those left outside or grown from cuttings. This suggested that the roots needed some time to settle and start taking up nutrients when they were planted outside the following year.
However, all the fuchsias overwintered this way quickly put on good growth when they were planted outside in the early summer. If you don't have a greenhouse, try keeping them in any frost-free area where there's plenty of light. 

Other methods we tried

Fuchsia cuttings

We took softwood cuttings in August and potted these on in spring of the following year. They did well, but the plants took a long time to establish.

Mulching fuchsias

We mulched some of our fuchsias with bark chippings and this worked well in Yorkshire, but we lost all our plants in Glasgow. This was probably due to the cold, wet clay they were grown in, which made the mulch very wet.

Interestingly, in Glasgow we left a few extra fuchsia plants in the ground with no mulch and these came through the winter unscathed. We think this was because the crown of the plant remained dry compared to the mulched plants.