I would suggest starting with Carbide Create, which I started to cover above — the problem is, it lacks an offset path functionality, so one would need to do this by hand, and it would require that one do the mathematics to determine where objects go and what size they are.
EDIT: it will also be necessary to manually add rounded corners, a technique for this is shown in: http://www.shapeoko.com/wiki/index.php/Carbide_Create_Photo_Tracing — you really should start on some simple tutorials first. I believe if one only does paths with such suitably rounded corners no additional math will be needed.
The best free drawing program is Inkscape (if you have a Mac you may want to consider Cenon) — both of these are vector drawing programs and want one to understand Bezier curves and their on- and off-curve control points. If you have access to a copy of Macromedia Flash, it’s a nice alternative.