To correctly answer your questions, we need to know two things; specific model of machine and what operating system version is installed.
Assuming that you are running Mac OS X of some flavor, you can find out both pieces of information by first clicking the Apple menu and selecting "About this Mac" wuich will bring up a small dialog box like this:
By clicking the "More Info..." button, you will launch System Profiler, which would show the following from a Titanium 1 GHz Powerbook:
The important model information will be found in the Machine Name and Machine model information.
Now, you can sort of "reset" you computer to go through a full initial interrogation, as it would do the first time it was powered up after the OS is installed. This requires that you boot into single-user mode by powering the computer with the cmd-S key combination held down until you get to the black dumb-terminal Unix console screen.
Enter the following commands exactly:
/sbin/mount -uw / <enter>
rm /var/db/.AppleSetupDone <enter>
shutdown -r now <enter>
Your computer will reboot and think it is a virgin and guide you through the process of setting up your own Admin account. Be sure to include the period before AppleSetupDone filename.
At this point, you will have the older owner's home folder in the Users folder on the root volume, which you might want to hang onto in case there are some preferences or application support files for certain applications that should be moved to your home folder.
Finally, once you know the Machine Model information, you should be able to find the appropriate battery at several vendors. One I have used is OWC and you can start at this link. You should also locate the model number on the bottom case of the PowerBook for correlating with the info on the OWC site.