Fuchsias usually root easily Bbpostbox. There are lots of methods that work. This is what I usually do.

Pull off some non-flowering side shoots about 3" - 6" long. If you can't find any without flowers, nip off all the flowers and flower buds.

Strip the leaves off the lower half of the cutting

Get a pot of damp compost and push the cuttings down the sides of the pot, all the way round, so they're half in, half out.

Pop a clear plastic bag over the top of the pot, arrange so it doesn't touch the leaves if you can and secure it with a rubber band round the pot.

Put it on a bright but not sunny windowsill and hope that they take.
Good luck

i do the same but keep them in semi-shade. I mist the cuttings (with water) every day, to keep inside the plastic humid. Take great care not to damage the cuttings when planting. As long as they don't dry out they should take.

If you can, arrange the plastic bag so that it doesn't touch the leaves. Fuchsia cuttings will also root in water - prepare the cuttings in the same way as for putting in pots. Try both ways and hopefully at least one will work. I find they root more readily in the early part of the summer.