On a new computer, if you just installed iTunes, the library is empty.
Syncing content with iTunes is generally one way, from computer to iPod. You cannot transfer song files from iPod to computer using iTunes (except for songs purchased from the iTunes Store). However, there are third-party methods and utilities that can transfer from iPod to computer. If you do a search on something like "ipod transfer," you should get some links.
Once the song files are on your computer, you can add them to the iTunes library.
NOTE: Songs previously purchased from the iTunes Store can be re-downloaded at no cost, from the iTunes Store Purchased screen.