Basically you scan it, and manually trace and color it as a vector graphic via a program like Illustrator or FreeHand or Sketch.
If you have no idea what that sentence means, just hire a graphic artist for a few hundred dollars to do it for you. Depending on the complexity of the graphic, it can be fairly labor-intensive and might take you dozens of times longer to learn how to do it (and do it poorly) than it would take a professional graphic artist to do it.
Once you have the vector graphic, you can "print" it as a raster (pixels) graphic at any resolution for things like email attachments. Print shops will be able to handle the vector graphic directly for things like letterhead and t-shifts. In fact, they're probably a good...