Obtain a fresh sheep skin. Check with anyone who raises sheep for meat. Even if the sheep are being raised for wool, perhaps you can arrange to purchase the skin of one who has dies from natural causes, although you may have to do the skinning yourself.
Soak the hide in a basin full of cool water. Change the water each hour until the blood appears to be gone.
Wash the skin in cool water using a small amount of soap powder to remove the grease. Rinse well.
Scrape away all of the flesh left on the skin using a serrated knife. Drag the knife across the skin at a 45 degree angle until all of the flesh is scraped off.
Dissolve 6 lbs. of potash alum in 6 gallons of cold water. Dissolve 1 1/2 lbs. washing soda and 3 lbs. salt in 3 gallons of cold water and add to the potash alum solution slowly, stirring well for a full 5 minutes.
Immerse the sheepskin in the solution. Let it soak for two to five days or up to a week.
Remove the sheepskin from the tanning solution and wash it in cold water with a small amount of soap powder, rinsing very thoroughly. Lay it flat to allow the excess water to drain away.
Coat the skin side (not the fleece side) with neatsfoot oil, covering all of the flesh. Let the oil soak in for an hour, then apply another coat. Cover the skin with plastic wrap and let it sit overnight so the oil can soak in.
Work the skin side across a hard surface like the back of a chair in order to make it supple. It needs to be worked a few times a day while it is drying.
Trim the rug if you wish. Lay it on the floor and enjoy your new rug.