How do I convert a jpeg to a vector?

If you have Adobe Illustrator CS2 or above, you can use the built in "live trace" feature. Just import the image into illustrator, then you'll see a toolbar at the top, click on "live trace" and illustrator will try to convert the image from bitmap to vector as accurately as possible. If that doesn't work, you can always use the pen tool to trace the image and then fill it in.