With 1.25gb of RAM, I'm guessing that you likely currently have a 1gb stick and a 256mb stick. As others have said, upping your ram to 2gb(by replacing the 256mb stick with a 1gb) will make a big difference.
Currently, there are a bunch of 1gb PC-3200 SO-DIMMs(which should work fine even though your computer will officially call for PC-2700 or PC-2100) for $15 and under on Ebay including shipping. There's at least one right now for $8.90 with free shipping. If you want to be completely correct and use PC-2700 or PC-2100, you might need to shell out $20 for a stick.
Whatever you decide to do, I think that this is a good and inexpensive place to start.
That 256 MB is sodered on. Only upgradable RAM is the second slot. He already has maxed out the RAM at 1.25 GB.
Oi this thread went way off on a tangent, so once again, just turn off all Leopard eyecandy. ALL of it. Altemose, eyroungren et all have already shown everyone every trick there is to do. Leopard will then be nearly as fast as Tiger with a lot more current OS and software choices. Like Leopard Webkit, the last SeaMonkey PPC etc. Accept it is an old machine, don't expect it to do what a current Macbook Pro does, and you will be happy. Reasonably happy.