Your dahlias will continue to bloom prolifically right up to the first frost.  A heavy frost will kill the above portion of the plant and leave you with a decision on your next step.

You can do nothing with the plant.  You will then probably need to plan on buying new dahlia tubers in the spring for the following year’s plants.  Alternatively, you can dig the plant up and discover that the plant has produced a half dozen or more tubers like the one with which you started.  If you wish, those tubers can be stored and grown by you and a couple of friends next spring!  Amongst local gardeners, there are a number of methods for harvesting dahlia plants followed with varied levels of success.  For more information on harvesting and storing your tubers, go to ADS’s Dahlia University.  This web site has a lot of excellent information.