How do I actually put my Itunes songs onto the cloud?

You can't put your own songs into the cloud unless iTunes Match is available in your country and you subscribe to it : http://support.apple.com/kb/HT4914 (it's $24.99 per year in the US)

Without iTunes Match, whether music that you buy from the store will show for redownloading will depend upon what country that you are in (it's not available in all countries), and whether the music remains in your country's store (record companies occasionally remove songs/albums) - ideally you'd be keeping and maintaining your own backup copy of all of your downloads.