Hi spawn,
The easiest way to get fonts off your old Mac is by searching, collecting and copying to an external drive (if not networked). You can use Font Book to search-out and collect fonts. Once collected, copy them to the external drive and transfer them to your new Mac.
I recommend using Suitcase Fusion since it seems to be the most up-to-date utility right now. Font Book is okay, but not really good for agency production. I also suggest moving to only OpenType fonts for both quality and compatibility reasons, plus you get expanded character sets. If you're doing actual paying work, stick with mainstream quality fonts...I can't urge that enough. I see a lot of ads created with crap fonts that cause so many problems at print, pdf, web stages.
Here's a very useful Font guide Apple did for Tiger:
http://images.apple.com/pro/pdf/L311277A_FontTT_v4.pdf
Well worth the read if you want to learn more about font management on Mac. Font management can be messy, so the more you know, the fewer problems you'll have.
Good luck!
TTE