Before placing the slipcover, lay some rug-grip material on top of the couch cushions to help keep the cover in place.
Put the slipcover on the sofa, tucking it in well.
Roll up two old magazines, or more if needed, using rubber bands to secure them.
Push the rolled magazines into the spaces between the seat and each arm of the couch. They will help anchor your slipcover but be hidden from sight.