I unscrewed the seat bases, took off the old coverings and padding and used some cotton batt that I just happened to have as well as some fabric that I've had for probably six years. I used our staple gun to secure it to the bottom of the seat bases, cut off the extra, and screwed the seats back onto the frames. It took me less than an hour total and made such a difference.
Since there are two chairs, I took pictures of what one finished looks like next to the one I hadn't done yet. My daughters wanted to sit in the chairs for the pictures, but neither wanted to sit in the unfinished chair, as you can see below. They're both happy now that they each have a nicely re-upholstered chair to sit in.