To spend something in a weekend, practicing on the drawing will take you for hours. Just preparing your scan or photo so that it translates best in Illustrator. You can think about 3D effects, shadows, and adding the perfect color palette. Digitizing and lettering by using Image tracing is recommended in Illustrator. It is a great way to capture the quirkiness that comes inherently with hand lettering while still allowing it to be scaled up to any size without losing image quality since the result is vectorized art.
To take your designs from paper to digital with this method, you need your work to be completely finished. Quick pencil sketches or really rough work just won't cut it. Your work should be colored in, preferably in black, and be on a clean piece of paper. To bring your art into your computer, you can either use a scanner. Or you can use your camera phone.
Finally, Adobe Illustrator and Photoshop. While Photoshop isn't necessarily needed, it is best for preparing your scan or photo so that it translates best in Illustrator. (Tracing)