Usually in just a few minutes but sometimes the system seems to bog down a bit and it may take a few hours. It's usually just a few minutes though.
When it comes to changes that are in some way 'mission critical' to an advertiser (as for example pausing and resuming campaigns in cases in which it really matters), I'd say always give yourself at least a half-hour window. In other words pause at least a half hour before the ads must not show any longer, and resume at least a half hour before they must show again.
As skibum says, it's quite often much shorter - but if it really matters, it's best to think ahead a bit.
AWA