On your OLD computer, copy your "i tunes" folder....usually in My Music, to an external HDD.
Then de register that installation of I Tunes through the menue system. (you are only allowed 5 installs active at any one time).
Now on your new computer with its new install of I Tunes, register it, again, through the menue system.
Now copy the CONTENT of your old itunes folder into the new itunes folder. When asked if you wish to overwrite the original content...agree.
You should now have a working I Tunes with all your old music, apps or whatever.
You can now sync your Iphone, I pod, I pad or whatever.
Just remember to use the same details for your activation on the new machine as you hsad for your old machine. And provided you haven't exceeded your 5 install limit all will be well.