Loosely drape the fabric over the chair. Gather the fabric around the back section of the chair by pulling loose fabric from the front toward the back and holding the edges so that you have a flat piece of fabric on the front of the chair. Pull the corners and edges to the middle of the back of the chair to estimate the amount needed to cover the back. Cut off the excess portion of the fabric. Repeat the process for the seat by draping the fabric over the seat and gathering it on the bottom to judge the amount needed to cover the seat. Cut off the excess.
Lay the back fabric face down on a table. Arrange the draw-string in a circle 4 inches inside the edge of the fabric. Pin the string in place from the opposite side (the face side) of the fabric. Fold over the edge to create a pocket where the draw-string will sit. Tape the edge down with fabric tape. Leave 4 inches of draw string hanging out the ends and cut off the rest. Repeat the process for the seat cover.
Leave the safety pins in place until after you lay the cover over the chair, so you don't lose the drawstrings inside the cover. With the back cover in place on the back of the chair grip the strings then remove the safety pins. Pull the strings tight, adjusting the fabric so it is smooth on the seat-side and the rumples are on the back-side. Tie the strings with a shoe-knot. Repeat the process for the seat.