No Apple operating systems besides the ancient System 7.6 and previous (won't even run on the G3 iBook) are free. You cannot legally obtain Mac OS X (any version) for free, unless someone simply gives it to you (which entails a legal license transfer -- downloading off the internet does NOT meet this requirement).
Yes, simply pop the 10.4 installer CD/DVD into the drive and the machine should boot from it. You can help it along by holding the 'c' key as the computer boots, then it's a matter of clicking through a few dialogs to install Mac OS X.
If you have trouble with the installer failing to recognize the hard drive, it could be due to the GUID partition scheme you applied -- in this case, simply open Disk Utility when booted from the CD/DVD, and reformat the drive with APM or "Apple Partition Map" partition scheme, then try the install again.
Looks like you're going to be spending more than $100 on a set of 10.4 install disks:
http://lowendmac.com/deals/best-mac-os-x-tiger-prices.html
...they can be had on eBay for much less, but be warned: be very wary of what you get. If you receive gray-colored disks, more than likely, they're system-specific disks that will not be able to be used with the iBook G3. You want
retail disks, which you'll have to specifically ask the seller if they are or not.