I suppose it depends firstly on whether you let itunes sort your music for you automatically into its own folders etc, or whether you just have a link to your music all over the place on your computer.
If you let itunes do it for you, then the easiest way i found was to simply get a external hard drive and get the itunes music folder which contains the library file and all of the artwork and music files etc. Then simply put all of this into the new computer into the Music folder that was on your old mac. (You could also do this via the network, as in create a shared folder and transfer all of the files that way)
After youve done this, you need to open up itunes whilst holding down the 'Shift' button and select 'Choose Library...' then select your own library that you have put into the music folder.
Now when in itunes go to Itunes Preferences then select the 'Advanced' tab and then where it says 'Itunes Music Folder Location' select 'Change' and chose the music folder where your music is contained and your music should now be on the computer and fully working.
You may also want to Authorise the computer so that you can use music that you have bought off of itunes, this can be done by selecting Store then selecting Authorise Computer.
Hope that helps and isnt too confusing!