Sprinkle the stain with finely sifted flour, then lay a piece of brown paper (from a clean paper lunch bag or shopping bag, for example) over the stain and stack phone books, bricks, or other heavy weights on the paper. Wait about half an hour. Remove the weight and the paper, and then use a clean whisk broom to sweep the flour out of the carpet. Repeat the process as many times as necessary to soak up all the grease, using fresh flour and paper each time.
Adapted from "101 Old-Time Country Household Hints," © 2008 Publications International, Ltd.