I had an old iBook G4 that could be useful for an elderly person, to be able to do her banking and basic internet browsing without having to use an XP-vintage, molasses-slow, honeypot-aspiring PC.
There's a reasonably complete and up-to-date guide in https://ricanlinux.blogspot.com/2015/03/ubuntu-mate-on-my-ibook-g4.html. I had to change a couple of details; and there are a couple of practical considerations to be had.
(Note to self: "lightness" in Linux rather correlates to "barebones" ,
which correlates with "hardcore" (text configs, mailing list scouring,
lots of googling). Next time I'll be trying a heavy-weight distro for
this kind of thing; better slow-but-useable than less-slow-but-WTF.)
To prepare the pendrive, it's enough to copy an Ubuntu-like ISO into the drive (block-level), so this can be done in OS X, even Windows has some application for that.
sudo dd of=/dev/YOURDISK if=/full/path/to/YOURISO bs=4m && sync
(but cat YOURISO > /dev/YOURDISK should work, too)
Now, to boot, go into Open Firmware and use something like
X = 0 or 1 depending on your USB port, Y = 2 (partition number) in my cases.  
The screen should flash a bit, some text should appear and scroll. Congrats, you're already booting Linux. (as of 2016, remember to at least use radeon.agpmode=-1 in the yaboot prompt! more details in the ricanlinux link, including a link to a depressing bug-report thread regarding the useless, misleading yaboot suggestion of video=ofonly. Without the agpmode switch, the computer will sooner than later start flashing the screen to black and hang. Might look related to heat, but no, can happen even when the computer is idle.)
Note, these initial steps worked for me for 2016 images of Lubuntu and Ubuntu MATE. It did NOT work with a Debian PPC "Small CD or USB stick" image; it failed with Open Firmware complaining that it could not open cd:\\yaboot (more or less, I can't remember exactly). I guess that some tweaking of the OF boot command would fix it (\\yaboot maybe?). 
I finally used Lubuntu because of its supposed lightness, but at the last moment (when seeing the recipient using it) I wished I had investigated a bit more into alternatives. Lubuntu seems pretty poor on the accessibility front; to even change the mouse double-click speed, I had to edit a text file and re-log in. Forget about anything like setting a minimal text size or whatever. I'm guessing that Ubuntu MATE would have been better... or maybe I missed some package, subsystem, distribution? What a mess. And yet, of course, thanks so much to the Linux community that there was something current to install at all, instead of the utterly-abandoned Mac OS X 10.4.
... speaking of messes... Lubuntu's support for polish keyboard was actually quite good, BUT if you install with one kind of keyboard with a goal to set another keyboard later, things get hairy. I'm guessing that if I had installed directly with the polish keyboard everything would have gone smoothly, but instead I had to go down a number of is-it-a-dead-end mazes, like fcitx, ibus, greeter options, lxkeymap, Keyboard Layout Handler applet for lxpanel. I'm not sure, but looks like what fixed things for me was to run "sudo
dpkg-reconfigure keyboard-configuration" (which anyway didn't re-run the
Very interesting for me: despite our internet-focused goal, the very first thing the grandma wanted to do instead was to see photos she had in a CD! Luckily it worked well enough - but again, being able to set all the system to use single-clicks instead of double clicks (in the file manager, for example) would have been good.
I spent some time trying to make video work, and it did, but the end result was about 1 FPS (Vimeo in Firefox), at least given the video config in the ricanlinux post; so probably that was a waste of time. YouTube behaved as if it was continuously buffering, never actually played. Cisco's OpenH264 plug-in was marked in Firefox as "soon to be installed" (strange-looking, maybe a bad polish translation? I never saw it finish.)
I set up unattended updates to happen at shutdown everyday for both security and normal updates, but they seemed to be acting up: the shutdown was taking about 8 minutes every time, and the list of updates stayed the same. The logs didn't show anything strange; there was only mention of something like "temporary translation problem" (?) for some ubuntu.pl (?) domain. I had to install manually in the last moment, and hope that it really was some temporal hiccup. Maybe configuring for updating during usage instead of shutdown would have been better, but I assumed it'd make the computer too slow and again had no time to actually test it.
And finally, it was surprising that this rather venerable (12 years?) iBook's battery was still alive and kicking. I didn't think to check how long did it work, but work it did. Lubuntu's lxpanel battery indicator didn't seem to even detect it.
 https://www.debian.org/releases/sarge/powerpc/ch05s01.html.en. Note, that was for Sarge (Debian 3.1), when Open Firmware Macs seemed to be relatively recent (!); the USB booting instructions got removed in Debian Lenny (5.0); current is Jessie (8) and the USB boot instructions for PowerPC continue to be missing. There is still hope anyway: someone reports success on Wheezy (7): https://lists.debian.org/debian-powerpc/2012/08/msg00042.html
 I really have to try installing one of those <200 KLOC SmallTalk systems Alan Kay talks so much about.