If you are currently working, you might get an offer early during Oct-Dec.
Your school should have a job/career fair during Nov-Jan.
You can probably start applying around Feb-Mar. But to be honest, you can apply at any point in time. But until you are done with rotations and know what you want to do, hold off on applying.
And you have to factor in residencies b/c midyear/applications come during Dec-Jan. So pretty much, you have to make a decision around Dec whether or not you want to do a residency/fellowship. ..Or you can just go to midyear, and back out of residency/fellowship after coming back (like what I did, but waste airfare, you can go for the experience).
But with the terrible economy (hopefully improving in the coming year), your job search will probably put you at least until graduation or after. A lot of my fellow 09 classmates are still looking...