Remove the slipcover, and look for the tag. Most slipcovers have a fabric care tag from the manufacturer on the inside, typically sewn into the inside seam. Read the tag, and follow directions written there. If the directions say "dry-clean only," drop off your slipcover at your local dry cleaner, or wash it at your own risk.
If there's no tag, examine the slipcover. Any kind of silk or wool should be handwashed or dry cleaned. If the slipcover has texture or detailing such as beading or burnout, do not machine wash it. Cottons, synthetics and linens can typically be machine washed without damage.
Any machine-washable slipcover will be both preshrunk and colorfast. To determine whether it's colorfast, rub a white paper towel or washcloth on a hidden part of the slipcover. If the color comes off onto the white cloth, it is not colorfast and should be dry cleaned. If you're not sure whether it's preshrunk, use caution, and have it washed professionally. If you wash it in a machine, it may shrink up and become unusable.
If you determine that your slipcover is machine washable or you decide to take a risk and try it, wash it with cold water on a gentle cycle, and hang it to dry. Put it back on your sofa when it's slightly damp for the best fit.