It can definitely be a bit tricky to get your Dahlia to survive the winter in climates where it can't grow outside. There are, however, some tips and steps you can follow to give your plant the best possible conditions:
Carefully dig up the tubers and shake off any excess soil
Cut down the stems to 10-20 cm / 4 - 8 inches
Remove old, damaged and soft tubers.
Cut off the small roots at the end of the tubers
Mark what type of Dahlia it is with some sort of name tag
Put the tubers in a tray or pot with peat, sand or cedar chips.
Care during winter
Store the tubers in a frost-free, cool (40-45 °F / 4-7 °C is perfect) and dark place. A basement or garage works perfectly fine.
Check the tubers once in a while to make sure that they haven't started to rot (and if so, immediately remove any mold or rotted parts to prevent it from spreading).
Don't water them until it's time to prepare them for spring.