You will be using an emulator called "Dolphin". This is a free, legal piece of software that is open source with a large community backing the project. You can always find the newest version of the program here.
There is a few ways you can get the files off the disk, including though your computer or via a Wii. Check out this wiki page for more info.
There are people that re-skin/re-model games in their free time. Communities of these people have gathered to this forum. Here are the games we have played with on stream:
After the first day of streaming, I was running into issues with video stutter and then audio popping/clicking. Many tests were had but the best we have come to so far follows...
What is the issue with chroma?
What is Dolphin