ibook G4

In order to identify the iBook G4 in question, you may want to have a look at, for example, https://everymac.com/mac-identification/.

Technical specifications and manuals for iBook G4 models can be found via Apple - Support - Technical Specifications and Apple - Support - Manuals (repeatedly click the "Load more results" button). Alternatively, see https://everymac.com/systems/apple/ibook/.

If the exact model does not have an installed AirPort Extreme card, (external) alternative solutions are also possible.

A USB Wi-Fi adapter could be one, but would require Mac driver software compatible with the operating system version installed (not always easy to locate, especially not for Mac OS X 10.3; for Mac OS X 10.4 you may find drivers for an adapter such as Edimax EW-7811Un).

A wireless Ethernet bridge (Netgear WNCE2001 and Linksys WET610N are merely two examples) could be connected to the Ethernet port of the computer. No special drivers needed. Some Wi-Fi range extenders (such as TP-Link RE200) do also have wireless Ethernet bridge capabilities.

Yes, it's wifi compatible. This page gives details for the operating systems Leopard (10.5) and Tiger (10.4):

https://arris.secure.force.com/consumers/articles/General_FAQs/MAC-OS-X-WPA-Wireless-Setup

While it is WiFi compatible, some iBooks did not ship from the factory with WiFi cards installed. These cards are limited to b & g protocols.

To see if the WiFi card is installed, you can click on the Apple menu in the upper left hand corner of the menu bar and press & hold the Option key which will toggle the menu entry "About this Mac" to something like "System Profiler". In the Apple System Profiler (also located in the Applications or Utilities folder), look in the left pane for the WiFi card and click on it to see if it shows the hardware details in the right pane.

IIRC, the WiFi card is located just beneath the keyboard which can be easily tilted up after using the two release at the top of the keyboard (these may need to be unlocked with a screwdriver). Be careful not to pull or tear the keyboard ribbon cable. You should either see the WiFi card or the empty bay with the antenna cable on the left side.

To configure the WiFi, you can click on the WiFi icon on the menu bar or access Network settings in the System Preferences (located on Apple Menu or in the Applications or Utilities folder).