First of all, I would say this would be if you are only really wanting to, as this could be a long process.
1. Use Safari to download TenFourFox. It is one of the only broswers that actually is built up to modern standards (it runs off of FireFox ESR).
2. You can either from here use hooktube.com, and stream directly to the computer. This is a secondary YT client that allows you to watch videos on a lower end system like the eMac. However, if the video is HTML5, it wil not run, and the embedding will let you know of that.
3. The other option involves downloading PPC Media Center and streaming to QuickTime. There are guides on the internet that can provide more information on that.
PS: UPGRADE THE RAM! 3XX MB is just not enough for anything to run on Tiger, let alone Youtube or TenFourFox. If you have DDR RAM then upgrades are cheap, and max it out.