The most important thing to keep in mind is to avoid cutting the canvas when you're ripping out a mistake. If you can't remove the mistake by "unstitching" with a needle in the reverse sequence they were stitched, you'll have to cut the stitches.

Once the stitches are cut, pull them out with a pair of tweezers. The kind you use to tweeze your eyebrows works pretty well. A tool called "Uncle Bill's" tweezers, available at your LNS and outdoor sporting shops, is also very good. The points are sharp and you can lift stitches with them without cutting the canvas.
In any case, relax, take your time, and look forward to getting it right the next time.