You probably is asking to rip your music to "Other" itunes library, because for the default library, after you connect and sync, all your music should be in itunes already.

If all your music are bought from itunes, then you can authorize up to five other itunes libraries on other computers, then the songs can be transferred automatically.

If your music are from other sources, then you probably want to search for 3rd party copying softwares, one suggestion is to use senuti.