Copy the entire iTunes folder to an external hard drive or flash drive (normally the iTunes folder is located under "My Documents" > "My Music").
Connect the external drive to the new computer and copy the iTunes folder to the exact same location it was on the old PC. If there's already an iTunes folder on your new computer, make sure it's empty before you replace it.
When you open iTunes, hold down the shift key.
In the new window, click "Choose Library".
Select the file "iTunes Library.itl" from the new iTunes folder.
Press OK to unfold the "old library" on the new PC.
That's it. Your playlists, music-files etc. are back in iTunes.