Remove the old cover from the high chair. Lay out the PUL fabric wrong side up on a table and place the old cover on top of it. Trace around the old cover to make a pattern template.
Cut out the cover shape from the PUL fabric. Use this piece to trace and cut another layer of PUL and a matching layer of batting or fleece fabric for the center of the seat cover.
Position one piece of PUL on the table wrong side up, then layer the batting or fleece on top of that and sandwich the second piece of PUL on top, right side up. Use small strips of masking tape wrapped around the edges to hold the three layers together.
Install a ball-point sewing machine needle on your sewing machine. Wind the bobbin and load the machine with polyester thread that coordinates with the color of the fabrics for your cover.
Insert the PUL-padding-PUL sandwich into your sewing machine. Stitch a straight seam all around the perimeter, approximately 1/4 inch in from the edges of the fabric.
Place the cover onto the high chair. Use scissors to cut slits in the cover wherever you need to in order to fit the seat belt straps through the cover, if applicable.