Itunes help please

I have just purchased a new laptop. i downloaded itunes and then plugged my iphone in,, it asked me to download an upgrade thn, backed up some files.
my problem is, i used to plug my iphone upto another computer, so all my libraries are on there. what i want to know is how i can get them onto my new laptop.
as none of my custom playlists appear down the side on my laptop.
any help will be much appreciated.
thankyou

 

i used the 1st above link, did everything it said, and also followed the instructions for keeping custom playlists, all this is set up,, but my phone still wont sync with my new laptop, it says it syncs, but for only 1 or 2 seconds, but no new music goes on to my iphone and NO error message comes up, i also deauthorised the old computer and have set my laptop as the only authorised computer to use itunes.
PLEASE I NEED HELP, THIS IS DRIVING ME INSANE!!!!!!

 

ive done all of that i think, it just wont sync on the new laptop, still syncs on old computer, but apparently u can only sync it on one computer. i saw a video just now, which showed how to edit some text using certain programs that would fool your itunes that your only plugging it into one computer, because you change a code to the same code as the old computer.
thanks for your help so far by the way.