Upholstering Instructions at Better Homes and Gardens. In a nutshell: Strip the chair of its original fabric and use the pieces as pattern. Then pin the pieces wrong sides out onto the chair. Remove pinned cover and sew it together, with welting reinforcing the seams. Put sewn cover back on the chair. It should fit like a glove!
DIY: FIRST TIME CHAIR UPHOLSTERY (includes 40 pictures with step-by-step tutorial)...if I can do it, ANYONE can. (P.S. - I had never sewn before this project). Website: http://snazzylittlethings.com/diy-chair-reupholstery/