Unlike Apple DVD Player versions 1.x that used a hardware-based decoding scheme for viewing DVD movies, versions 2.x and newer were software-based. The trick is getting the program to install on older, unsupported hardware. This web site has info and the necessary patch available to download. If you click on the "How to" link on the left, you'll find the page with directions for patching Apple DVD Player 2.2, the recommended version for use in the B&W G3s and Yikes G4s. I've successfully used the patched version of DVD Player in beige G3s with the stock 266 or 300 MHz G3 processor (running OS 9.2.2), and for the most part, watching DVD movies was trouble-free.
I found the Apple DVD Player 2.2 and did everything on that site, but ran into a problem.
The patched version gets to the splash screen, doesn't freeze, but it's not seeing the Apple CD/DVD Extension, even though it is enabled.