If you're in a cold area, then wait until the first frosts finish the foliage off, dig up the tubers and dry them for a while, then store them in dry sand or compost in a frost-free place. Start them off again in the spring in pots or trays and plant them out when all frosts have finished.

Some people in milder areas risk leaving them in the ground, but I live in a mild-ish area and lost most of mine last year. :-((

It is a risk leaving dahlias in the ground but I've lost far more storing them inside than leaving them outdoors( (perhaps they weren't dry enouigh inside because they went mouldy)

I've left dahlias in the ground for the past 10 years with very few losses ( North cambridgeshire/freely draining light soil)

Some of Kent's soil is clay - I wouldn't have risked leaving them in our garden there!

I agree, clay soil would almost certainly result in rotting off of the tubers over winter.