Are you talking about sharing the other computer's music library - or transferring it to your MBP? Sharing is easily accessed from iTunes if the other "online" computers have iTunes open and the permissions are granted. Shared libraries show up in the left hand column.
If you are moving your library....
You can only synchronize to one computer at a time, so if you want that to now be your MBP, you need to move your complete library to the new machine, wipe the iPod and reinstall from the new iTunes installation on the new machine (once you have authorized the new computer).
Before doing this you may want to copy all iTunes (not the ones from CDs) files to the MBP first - once you authorize the new machine you can do this and download all that music from the iPod to your MBP. However, that only works for iTunes purchases and not any music directly loaded into iTunes.
I am doing that now through WiFi at home with my new MBP - but have parked my current library on a network server first, making it easier. I am just copying all the music from there onto my MBP - and then will load it into iTunes and be up and running on the new machine.
Without the network server, you would just have to move the files through network shared folders in some fashion.
I have enough music files to fill my 160 GB iPod (and more) so this is not a trivial operation for me....
