If you want hibernate to work you need the following actions as root or with sudo
First check if the pm-utils package is installed (it should be by default).
# yum list installed |grep pm-utils

This should output something like :
pm-utils.i686 1.4.1-8.fc15 @updates

If you got no output you need to install pm-utils:
# yum install pm-utils

If pm-utils is installed yo need to edit the grub menu.lst file. I use nano to edit config files so i use:
# nano /boot/grub/menu.lst

Now add resume=/dev/swap-partition to the kernel line(s) in menu.lst. In my case the swap partition is /dev/sda4
So
kernel vmlinuz-2.6-something root=/dev/sda ro
becomes
kernel vmlinuz-2.6-something root=/dev/sda resume=/dev/sda4 ro

If your menu.lst file uses UUIDS the original kernel line looks like this:
kernel vmlinuz-2.6.something root=UUID=1c45aac9-f4c0-4a85-8154-c95fa5ac2554 ro

open another terminal and use the command
$blkid
This will give you the UUID from the swap partiton in my cas this is
/dev/sda4: UUID="076f3be3-495d-4d87-b825-27bd03551eb6" TYPE="swap"

Thus the kernel line in menu.lst becomes
kernel vmlinuz-2.6-something root=UUID=1c45aac9-f4c0-4a85-8154-c95fa5ac2554 resume=UUID=076f3be3-495d-4d87-b825-27bd03551eb6 ro

Now save the menu.lst file and try to hibernate.

Enjoy.