You will find the requirements for WPA (not WPA2) here:
AirPort Card: When You Can Join a WPA Network - Apple Support
With an iBook running an earlier operating system version, one would be limited to the WEP protocol mentioned by LaPastenague.
A USB Wi-Fi adapter with WPA/WPA2 support is not an option in this very case, since that would require special driver software (and typically at least Mac OS X 10.3 or 10.4), and the speed through a USB 1.1 port would be relatively low.
You could use an external wireless Ethernet bridge (also known as a gaming or media adapter) connected to the Ethernet port of the computer. Netgear WNCE2001 and Linksys WET610 are merely two examples. Some Wi-Fi range extenders (with an Ethernet port, such as TP-Link RE200) may also have similar bridge capabilities. A wireless Ethernet bridge does not normally need special drivers, and can thus be used under almost any operating system. Modern devices should support WPA/WPA2 security (check the specifications before you buy). However, for space, power and portability reasons, it may not be an optimal solution for a notebook computer.