Please see (although it's probably incomplete and at least partially outdated):
http://wiki.debian.org/Suspend
It indicates Debian's software suspend features seem to have been under major re-engineering lately, so it would be rather important to know the version of your Debian in order to provide accurate advice.
Software suspend does not need any specific hardware support: the only requirement is that there are no hardware components whose state cannot be saved and later restored.
If you want to suspend-to-RAM, apparently all you need is to have the appropriate packages installed and perhaps some very minor configuration (adding the -f option to S2RAM_OPTS if necessary, according to the link above).
If you want to hibernate (suspend-to-disk) your system, you may need a bit more work. If I recall correctly, the swap partition is used as a hibernation area by default, so your swap partition should be large enough to fit all your RAM (although the hibernation data can optionally be compressed, which may help somewhat).
MK
