dahlia tuberous root storage
Several extension sites tell how to do this. Dig the tubers after a frost has killed the top part. Cut top growth to about 2 inches. Shake all the soil off (or hose off) and dry completely. Some sites recommend a 2-3 day curing period. Then store in a ventilated dark container (box, paper bag) in something not-too-wet and not-too-dry (peat moss, vermiculite). Store at temperatures in the 40's to low 50's. Check them periodically for too dry (they'd shrivel) or too wet (they'd rot). If the temperature goes below freezing, they will freeze and die. If it goes into the 60's, they will "wake up" prematurely. Unfortunately, basements in modern homes are often too warm.
In the spring, you can wait until frost-free date, or you can pot them up earlier and grow them indoors for a few weeks to get a head start.
Here are some references: