Open the PDF in preview, go to the print dialog and you'll find some (hopefully) helpful settings — I say hopefully as I've not done exactly what you're after...
Click the little down arrow next to the printer name to expand the print dialog if its not already larger. In the bottom half of the dialog window, there's a drop-down menu where you can select a few relevant options:
- In Layout (in the drop-down menu), Pages per Sheet (you can set this to 2 to have a left and right side on each page)
- Also in Layout, Two-Sided (you can choose the paper edge over which the binding would occur — not sure how this works for folding in the middle though...
- The drop-down also has a section called Booklet Printing, which has various options that will be of interest to you, mostly the first checkbox to enable booklet printing :)
Now I've not done it myself, and I don't know if it'll work for folding the pages in the middle (it looks like its intended for binding the pages along one edge) but that's probably the place to start looking.
If it doesn't work as is, then you may need to manually rearrange the pages (which you can do in Preview) to be in the right order so that simple double sided printing with short-edge binding puts the pages in the right places, though this may be quite difficult if there's a lot of pages...
Good luck...