My sister got a used G4 laptop running 10.6 and, I think, the latest updates to other software. The video playback on YouTube is jerky, but the sound is fine.

What type of internet connection are you using? If the download is slow, that could explain it.

This aint going to happen. OS X 10.6 will only run on a Mac with an Intel processor and a G4 uses a PPC processor.

1. Your sister may have a G4 laptop running Mac OS X 10.5.6 but that is not the latest release of OS X 10.5 that honor goes to OS X 10.5.8 which is available as a free download here.
2. On the other hand if she has OS X 10.4.6 the last version of 10.4 was 10.4.11 and that update is available here.
3. if your sister has a Mac laptop with an Intel processor then she could be running either OS X 10.5.x or 10.6.x.
   1. If she has any version of OS X 10.5 (Leopard) other than 10.5.8 she should download and install the aforementioned updater.
   2. If she has a version of OS X 10.6 prior to OS X 10.6.4 that updater is available here
4. With any and all of these OS updates there are Quicktime updates that can and will improve the video performance.
5. If you could get the specific system information from your sister's laptop by clicking on the Apple menu > About this Mac then clicking on the More Info... button then sending along the Hardware Overview, that would provide us with some very helpful information for further troubleshooting.

I'm on wireless DSL.

I'll check out all the Mac's specs later today.

Depending on the generation of the G4 and the amount of RAM, that might be unavoidable. Watching YouTube videos is surprisingly processor intensive, and some of the original G4 systems, especially the first-gen systems, lack the grunt...particularly if you haven't maxed out the RAM.

If I recall correctly, the early G4 Powerbooks also had 802.11b wireless only, which will create a network bottleneck as well if you're using wireless.

Some specs:

ibook G4

Version 10.5.8
Processor 1.07 Ghz PowerPC G4
Memory 1.25 GB
VRAM 32 MB
ATI Mobility Radeon 9200
Quicktime 7.6.6
Firefox 3.6.7

I even see the same on my iMac G5 iSight maxed out with 2.5GB of RAM and running Mac OS 10.5.8: some streaming video from the web is jerky. In my case the net connection (Ethernet) may be involved as the same videos often do much better once downloaded. Other observations make me suspect the CPU as well, particularly when comparing the video performance of G5 with that of the Intel Macs on the same network. Between CPU, network speed and RAM there's ample opportunity for G4 and G5 Macs to 'underperform' with video tasks.

Well, that really sucks.

Your sister's iBook is an early 2004 model. It is maxed out on RAM and has the last software updates it is capable of. So far, so good but there is little or nothing that can be done with hardware or software to improve the video streaming. I can think of a few things you might try:

1. If she hasn't done so in a while use Cocktail, OnyX, or TinkerTool System to rotate all the log files and flush all of the various user and system cache files and buffers. Especially the internet cache files and buffers.
2. Try using another browser when accessing YouTube and see if that makes a difference. Run Software Update to be sure she has the latest version of Safari compatible with her iBook.
3. Shut down all applications on the iBook except the browser she is using to access YouTube. (Command+Option+Delete will show you all the active applications on the desktop and you can quit them from there)
4. While streaming a YouTube video open Activity Monitor (you will find it in /Applications/Utilities) and look at...
   1. System Memory at the bottom of the window. Particularly the amount Free and Inactive memory
   2. Look at CPU Usage. What is the % User and the % Idle?
   3. Look at Disk Activity and see what Data Read and Date Written are. (Note this will change every few seconds but look to see if either is remaining relatively high.
   4. Look at Disk Usage to see how much free space there is on the hard drive.
   5. Finally look at Network and see what that looks like. Normally it will be very spikey but the approximate average is what you are looking for.
5. Report back what you find -- in detail!

The biggest issue I see in that list is the lack of available RAM. Safari is RAM-hungry to start with, and decoding video is RAM-intensive as well. The CPU is capable of decoding streaming video, but I bet the system is RAM-starved.

1.25 GB RAM isn't enough?

You Tube looks a little better now in Firefox 3.6.6. Not so much in Safari 5.0.2 But that's true on my Intel imac as well.

Here's what I did:

Updated Safari
Updated Flash
Updated Security
Plenty of disk space

Ran Onyx:

checked SMART status
verified startup volume
repaired permissions (20 minutes!)--long list
Ran daily script
Deleted system caches (boot, international prefs, QT audio components)
Deleted internet caches (Browser, Download, browser history, recent searches)
Deleted font cache (system and users)
Deleted log files

1.25 GB of RAM is not enough when you consider your operating system is using at least half of that just to "keep the lights on."

Don't confuse your "plenty of disk space" with the free memory space. As Tacit pointed out above, what you are doing prefers more memory than disk space.