Cut down the flowering stems, but inspect first - sometimes you get little side shoots which will also produce flowers. Cutting them down often induces a second flowering, but make sure you let one or two spikes go to seed and shake them over the ground - that way, you'll get more foxgloves.

Thanks for your help Bamboo

The common foxglove is unfortunately biennial and therefore dies after flowering. Any new ones come from self seeding.
There are quite a few foxglove varieties which are happily perennial, such as digitalis lantana and d.ferruginea. Some of these have yellow or salmon flowers and are almost as pretty as the 'real' native digitalis.
I must admit that I felt cheated having planted up a whole bed with foxgloves which flowered wonderfully last year, to discover that not a single one came up this year.
Yet in the pebbles over a membrane by the back door, we have had a wonderful foxglove this spring that self-seeded from somewhere. I'm collecting the seed from this and will shake it around in lots of different places.