Has anyone reupholstered a chair?

Hello,
I found a chair I like to go with my new desk, its like a dining chair, but it needs reupholstering and it has one of those bases under the seat that is criss crossed belts. I know thats not the best way to describe it but my brain is really dead today (last exam yesterday woohoo) and I can't think what to call it.
I think I'm right putting in a seat pad on a dining chair, but this style I'm not sure of how to do it. I think you can buy the belt/webbing to replace the base. Then you would just staple gun it on under and crisscross it. But the inside is horsehair I think and sometimes these chairs have springs in. hmmm
Anyone done this before?
Any tips?