Can I get music on my iPhone 4s without purchasing them on iTunes?

Basically, can I download music into my iPhone like I do with my iPod nano?

For my nano I basically download mp3 songs and then go to my iTunes library and then add the songs into the library and sync and the music usually is sent to my iPod

I was wondering if I just do that for my iPhone as well, will it work? If not what else can I do?

Yes that'll work, even though there's a pretty high chance that the mp3's you're downloading are illegal.