In iTunes, click edit->preferences, then the advanced tab.
It'll show a path (like C:\documents and settings\username\my documents\my music\itunes\itunes music), which is where your songs are held.
Go there using My Computer, and see that all your songs are there (loads of folders with names of the artists that you have).
You can then just drag and drop that folder to a new drive, like an external hard drive or flash drive (if there's enough room). Then put it on the desktop of your new computer, and in iTunes on that computer, click file->add folder, and point it to that folder on your desktop.
(Before doing this, note that iTunes can sometimes link to files that are in other places, and so these songs won't be in the above place I talked about. To put all your stuff in that place, click advanced->consolidate library, in iTunes. In the preferences (advanced tab again), you may want to make sure that "let iTunes organise my library" is ticked.)