In order to hibernate, the system has to have somewhere on the disk to write the data that is in RAM to save it from extermination when the power goes out. There are other ways to do it, but not distros use the swap space for hibernation so as not to run into space problems on the hard drive. There is a kernel parameter to configure this, but you shouldn't need to go there.
The simplest thing would be just to create a swap file and enable it. Make it somewhat bigger than your ram. Say you have 4G ram, make a 5G swap.
$ dd if=/dev/zero of=/swap bs=1024 count=$((5*1024*1024))
$ mkswap /swap
Then enable it:
$ swapon /swap
And add it to fstab so it's enabled on boot:
/swap swap swap defaults 0 0
Lastly you need to tell the kernel when it boots where to check for potential hibernated data to boot too. In this case it needs to know where to find your swap file, so you'll need to add a kernel paramenter. You can find docs for this step in the kernel.org documentation.
Typically it would fall to the hibernate program to determine the exact location of the resume data and mark it in the boot loader.