How to transfer songs from iPhone to iCloud?

I have many songs on my iPhone but they are not on iTunes on my computer or in the iCloud. How do I move the songs to the iCloud/My iTunes Library from my iPhone? Is there an app I have to download for my computer or phone? Any help would be great! Also, I tried iTunes Match but when I activate it on my iPhone it just wipes all the music thats not in the cloud/my iTunes Library and I have to download it again. Any ideas? 10 points for best answer!

ICloud only saves songs that have been purchased through iTunes.