This is the best part, seeing your image come to life on the mirror! You must flip the acrylic over so the dull gray side is facing up. Don't try to engrave the clear reflective side, else you'll end up with a Ghost Image--which is a completely different type of effect (and a different Instructable, I presume).
IMPORTANT!! -- your image must be flipped (mirrored) to look correct from the front side. For Example, etching a word like "DOG" will come out backwards & confuse your poor pup.
You have several options for this step: draw something yourself with a marker; tape a black&white printout of your image onto the acrylic; send a digital image to a place that does engraving (check out Ponoko): http://www.ponoko.com/make-and-sell/design-it-yourself
Then, the fun part, grab your exacto knife or screwdriver (better yet, borrow a dremel tool!) and scratch away the lines on the back of the acrylic. I had a simple line art logo that only took me 20min. The screwdriver is good for removing large areas quickly, but not as accurate as the exacto for thin, fine curves. I'd suggest practicing a little to get your technique down before tackling a complicated image.
Wrist hurting yet? The laser engraving is sounding better & better now, isn't it?