You transfer songs from a computer to your iPhone by setting up an iTunes library for your songs on your computer. Then do a sync. You can learn more about these in the iPhone manual. There's a link to the manual in Safari on the iPhone and you can get the free manual in the iBook store.
Start iTunes on your computer. Make sure it is the latest version which is presently iTunes 11.
Use the View menu in iTunes to View Sidebar.
Set up your music and playlists in iTunes.
With iTunes running on your computer connect your iPhone.
Select your iPhone in the left sidebar of iTunes.
Select Music in the row of tabs on the right.
Select to have all your music copied to the iPhone or select to have only certain playlists copied.
Click on Sync or Apply