it can vary greatly for everyone. after our first son died, i was still producing some small amount when i got pg again 7 mos later. with our second, he nursed for 2 years and when he was done i produced the tiniest amount for a long time.
when we lost jesper, i was told to drink sage tea. it helps dry up your supply. i found some blackberry sage tea (for the flavor of something other than just sage) and then added dried sage leaves from the spice aisle when i brewed it. it took care of the engorgement and major production of the early weeks. i think by the time i got my cycle back (at 12 weeks post-partum) i was at the very low level of production that held until i got pg again.
cold cabbage leaves against your skin (under your bra) help, too. once they are warm and floppy, switch them out. it shouldn't take too long. a couple of days maybe.
really, you are already well on your way. simply not nursing and not expressing anything will trigger a shut-down. the methods above (and binding--which is uncomfortable for me) will speed it up.
hope this helps.