This barstool reupholstery tutorial will show you not only how to reupholster but how to avoid crooked welt and shifting fabric. 
1. Take the seat off the frame by unscrewing the two screws holding the plywood platform onto the base.
2. Remove the old fabric by prying up the staples with a flathead screwdriver or staple remover.
3. Cut a new top piece of fabric…I have a very easy and accurate way to do this step in the video.
4. Sew the welt onto the top piece of fabric. Make sure to either pin the welt onto the platform or sew it on with the welt against the feed dog to avoid the fabric shifting(this is explained in detail in the vid).
5. Cut the boxing piece to go around the platform, pin the boxing to the platform and sew it onto the welted platform piece.
6. Turn the fabric right side out and install onto the foam and plywood base. This is somewhat difficult because the fabric is tight. If you put a plastic bag over the foam it makes installation of the fabric much easier.
7. Staple the fabric to the bottom of the plywood platform and install another welt around the bottom edge of the plywood. 
8. All finished…now you just have to reattach the seat to the barstool and enjoy your beautiful new barstool.
