THAT is a loaded question because there are so many variables...
Let me give you a range of possibility.
First you must file an application and get a permit for your project to ensure you are not later in a precarious position and perhaps forced to undo what you started. That being said, from the lowest, being and addition on top of a pre-existing foundation, like over a garage, with no bells and whistles (no plumbing, complicated ectrical and minimal inexpensive windows, you can start at $150 a square foot (@$13K with just the basics for a thrifty box)...now go the detailed and more structurally complex and begin by doubling this, so if you need to dig & pour foundation, want plumbing, nicer windows, internal walls/doors, hardware fixtures...20 - 50K depending on the scope of your project, if you are doing wood shingled roof, copper gutters, french drains, Pella windows, Stickly cabinetry...well, sky's the limit!
Now if this is an add-on element, today's modular pre-fab options may surprise you both in high quality and levels of finishing and they start around $90 a foot!