The first things you should do to speed up your iBook is to max out the RAM to 576MB (or 544MB) and to pull out the old HD and put a new one in.
Apart from these modifications, people tried to speed up their iBook by overclocking the CPU and the GPU (Graphics Processing Unit).
Since there is no fan but only passive cooling elements to pull away the heat from the chips, they will get hotter as usual which shortens their life.
Therefore i do not recommend overclocking. For documentation purposes i will provide some links to sites with instructions.
Graphics acceleration
Some users try to speed up the built-in ATI Rage Mobility Clamshell iBook graphics by the software overclocking tool ATIccelerator II
The program runs on MacOSX 10.3.9 and above. The clock frequencies are set separately for the GPU and video memory.
Since the ATI Rage Mobility graphics is not officially supported by ATIcceleratorII, the only thing that seems to have an effect is overclock the video-ram.
Additional links:
iBook G3 overclocking (german / english google translation))
Reader feedback on ATIccelerator II (english)
There you will find reader reports concerning PowerBook Pismo, which also has an integrated ATI Rage Mobility chip.
CPU overclocking
You will need some soldering experience and special tools to start with CPU overclocking. You have to locate some tiny resistors on the logicboard and solder them to a different location depending on the decided overclocking values. It is recommended to choose the next higher value, otherwise you will get Kernel Panics.
Detailed description on mactech.com, 366mhz no firwire (englisch)
iBook Firewire tuneup (english / japanese)
Overclock iBook no firewire ( french)