For example, release the new design on new.reddit.com and let viewers migrate over to it at their own pace.
Once you have a lot of people using the new reddit instead of the old design, you can migrate the old reddit to old.reddit.com and put the new design up as the default.
WHATEVER YOU DO, DON'T GET RID OF THE CURRENT DESIGN, until you have adoption for the new design. Period. If you simply replace the old with the new, reddit is as good as dead.