Using one supply for two fans is no problem. The easy way would be to make two identical fan and speed controls, as if you were making two completely separate stir plates, and then connect them both to your power supply in parallel.
Did you use the LM317 (or similar regulator), like on the page you linked? If so, that means you'll assemble two of those circuits, then connect the "12 v in" wire of each to the positive side of your power supply, and the 0v wire to the negative side of your supply. You may want to put a switch on each section, but you can also just leave the speed knob turned all the way down on the side you aren't using.
As far as supply current, you will be drawing twice as much, so you'd need to get one of appropriate size. I just tested a fan on my bench supply, and it drew about 250mA (0.25A) at 12v, so for two of these fans you'd be drawing 500mA (your fans may be different, it's best to check with a meter), and you'll generally want to oversize your supply. For 2 of my fans, I'd probably go with at least an 800mA supply. If you don't have a multimeter to check with, you'll probably be ok with something that big or bigger.
If you need clarification on any of that, let me know and I can draw out a diagram for you.