Home & Garden TV has several suggestions for making disposable chair covers. The simplest suggestion is to use pillowcases or T-shirts, and just slide them over the chair backs. Tie a bow around it to make it more festive. Alternatively, use cheap fabric and fabric glue to build slipcovers. Measure the chair backs, cut the fabric to size and glue it together.
Cover most chairs easily with only two pieces of fabric. Home & Garden TV suggests cutting two pieces of fabric. One drapes from the top of the chair back to the floor, and the other covers the front of the chair back to the seat. The two pieces can be glued together while inside out and then turned right-side out to hide the seams. For a more finished look, trim the remaining raw fabric edges by gluing them down. Slip the cover over the chair back, and if desired, tie a festive ribbon around it. Use heavy paper or a plastic material instead of cheap fabric for disposable chair covers.
Craft, Interrupted suggests buying disposable plastic tablecloths, which come in a wide variety of colors, and cutting them into four pieces. Then, use each piece as a chair cover by simply tying the plastic onto the chair using a fancy bow.