windows xp or 2000 i assume?

Right click start button, go to explore (this makes sure you are in the right profile) use the "up" arrow button to go up a level into C:\Documents and Settings\<your username> then go into favourites folder. highlight all the links and folders, then right click and copy.

Then paste them onto a usb pen drive or burn them to cd, and transfer to new pc (do the opposite way round, copy and paste into C:\Documents and settings\your username\favourites on new pc) . voila