Among other things, hibernation will only work if all hardware supports
hibernation. In particular, the video drivers must support this feature. I
needed to load more recent drivers for my NVIDIA card before hibernation
would work.
Additionally, you have to turn on the hibernation option using the hibernate
tab of the power options properties window, accessed from the display
properties screen savers window. Then, you need to use the power schemes
tab of the power options properties window to set a finite time delay before
hibernation.
Unfortunately, even if you get hibernation to work, you may wish that you
had not. I finally turned it off, since about one out of ten times when the
PC woke from hibernation it immediately dies with a blue screen. This might
be specific to my PC and peripherals, but I have not had a single blue
screen since I turned off hibernation.