I have a iBook G4 (PowerPC G4) with CPU Speed 800 MHz. This is running Mac OS X 10.3.9 and it is very slow. What can I do to it to make it faster and cope with new version of Mac OS X? Can I do this myself and if so where is a good source of advice/help

Your computer cannot run the new version of OSX which is 10.6. PowerPc s can run Leopard (10.5) at the latest but need a CPU of 867 MHz which yours does not have. The speed issue could be addressed as a basic clean up and tidy up of system file check, repair permissions, eliminating assorted cruft which has collected over the years of use. For that there can be lots of help but the initial motivation for upgrade is ill-founded. Your computer could be upgraded to Tiger (10.4) but that still puts you woefully behind the current set of features and will certainly put you further behind once Lion (10.7) is released. Perhaps this is the moment to consider a reliable back up of important personal data, then a clean re-install of OS from your original install disks with the intention of a sale of the older hardware. Think over your situation and re-post about your needs. Spring clean up is possible; upgrade to "cope the the new version of Mac OS X" is not.

A couple of questions: now much RAM is in the machine and how much free space in the hard drive?

You realistically would not want to go any farther than MacOS 10.4 Tiger, as 10.5 Leopard is beyond the reasonable capabilities of your machine and even with third-party "tweaks" that allow installation would still run more slowly than Tiger on your machine. Of course, 10.6 does not run on anything but the Intel processors, so that is out of the question.

You can speed things up a little bit by putting in a faster hard drive than the (probably 4500 RPM) drive that came with the iBook. I noticed a speed increase even going to 5400 RPM, and you can get even 7200 RPM drives for that computer. If you have less than about 10 or 15 Gbyte of free memory on your HD you probably would begin paying a performance penalty with Tiger. Reasonably, going to a larger 5400 RPM drive might make sense.

You can put up to 640 MByte of RAM in your machine. I see OWC with a 512 MByte stick for a reasonably small price, so there should be other suppliers out there with similar deals. Maximizing the RAM can be a big upper in machine speed, as the system is spending less time doing page swaps with virtual memory.

That being said, no matter what you do, this machine will likely still feel somewhat slow, even surfing "normal" websites without a lot of Flash content. My TiBook, with 1G memory and a 160 GByte 5400 RPM drive is definitely not swift these days. But then again, both your and my machines are nearly nine years old, which is several geological eras in computer time.

EveryMac.com reports that your iBook can be upgraded to over 1 GB with a 1 GB RAM module.

Instructions for replacing the RAM card can be found in this PDF:

http://www.info.apple.com/usen/cip/pdf/ibkg4/ibg4-mem-cip1.pdf

The best you can do with the OS is Mac OS X 10.4.11. You can get by with an upgrade disc since you have Mac OS X 10.3.9 installed.

Sometimes you can find a good deal on it on eBay.

http://cgi.ebay.com/Apple-Mac-OS-X-10-4-Tiger-Upgrade-DVD-w-manual-/270738580917

As old comm guy suggests, it's important to check on the available space remaining on your hard drive. The general rule of thumb is that you need 15% of the total size of the drive remaining as free for optimal performance. If you have less than that, it can be a cause of the slowdown you're seeing.

Check out Dr. Smoke's tutorial on Freeing space on your Mac OS startup disk for more information.