The sync system really just copies stuff from your iTunes library to your iPod. It's one way.
If you buy a new computer, the procedure is to somehow copy the music on your old computer's iTunes library to the new one. You can copy the music onto a DVD, hard drive, or just use the iPod itself with a free program like Yamipod.
Once your new iTunes library looks like your old one, with all your music on it, then you can connect your iPod and sync with the new library. It will erase all the songs on the iPod, but this is now OK since they're all on the new computer anyway.