OK,
On old computer, click on your first Playlist
go (F)ile, (L)ibrary, (E)xport playlist
name your playlist nixplay01.xml (selecting XML format) when the save dialog comes up
Save it on a memory stick
Take memory stick to new computer
In Itunes go
(F)ile, (L)ibrary, (I)mport playlist
select nixplay01.xml and import
Voila!!