How to make APM work
You need to enable the APM Power Management support in the kernel and install the apmd to handle the events triggered by the kernel driver. The configuration for what to do at the different events is done in the proxy script which is usually found in /etc/apmd_proxy. See man apmd for further information on this.
Screen blanking (Standby)
apm -S will standby the machine. Fn+F3 should result in the same thing.
Suspend to RAM (Sleep)
apm -s will suspend the machine. Fn+F4 should do the same thing.
Suspend to disk (Hibernate)
The Phoenix BIOS allows you two ways to hibernate with APM: using a special partition or using a hibernation file on a dos type partition.
using a hibernation partition
The partition to be used for hibernation must be a primary partition that is at least as big as your laptop's memory including its video ram. First set the partition type of this partition to a0 (IBM Thinkpad hibernation) with fdisk, and then use tphdisk to write a hibernation file directly to this partition.
Only follow these instructions, if you understand them. You will overwrite a partition on your hard disk and might loose valuable data - consider yourself warned. For example, assume that /dev/hda2 is the partition that is to be converted to a hibernation partition. Become root and type /sbin/fdisk /dev/hda. At the fdisk prompt type t to change the partition type, then type 2 to indicate that you want to change the type of partition 2, and then enter the partition type: a0. Now type w to write the partition table back to disk and exit. After that use tphdisk to initialize the hibernation partition. First estimate the size of your laptop's memory (main and video). For the sake of this example, let us assume that the main memory is 1024 MB and the video card has 128 MB of memory. Then the command tphdisk 1152 > /dev/hda2 will initialize the hibernation partition. Note that this will only work if the partition is big enough. After a reboot, Fn+F12 will work as expected.
I have successfully used this method on a T41 (2373GEU) that runs Fedora Core 3.
using a hibernation file on a dos partition
The partition to put the file on must be a dos or vfat partition. Fat32 formatted partitions have been reported successful as well as Fat16 formatted ones. The file is either created with phdisk.exe, if you happen to have a floppy drive and a bootable dos floppy disk that you can start it from. Under Linux tphdisk will do this job for you.