How do I backup my old games to my new wii?

Ok, I just bought a new wii because my old one broke. as some people know, if you play your games on a new wii they make new data for the new console. I need my data back from my old games. there is a way i heard that you can take the memory thing out of the broken wii and put it or hook it up to the new wii, therefor giving me back my old data. I really would appreciate some help with this....