Launch iTunes. Insert a blank CD or DVD into the computer's CD or DVD burner.
Click the "File" menu. Hover the mouse over "Library." Select "Back up to Disc" from the menu that appears.
Select the radio button next to "Back up entire iTunes library and playlists."
Click "Next." If your iTunes library is too large to fit on a single disc, iTunes pops up a window notifying you of this. Click "Continue," then insert a new blank disc when prompted.
Launch iTunes on the computer to which you want to move your library. Insert the first backup disc into the new computer's disc drive. Click "Restore" in the window that opens to switch your iTunes library to the new computer. Insert the additional backup discs as prompted.