Easy for Some
It may seems like an insanely easy part of the iPhone and iPod experience, but new users who are not as exposed to technology often have trouble getting music on their phones. Taking your CDs and getting them onto your new iPhone is crucial to take advantage of the technology and it is easier than it seems. All it takes is your computer, you iPhone, and your iTunes account.
Ripping the CD
Take the CD you want to put on your iPhone and put it into your computer. If iTunes is not your automatic music player you may have to go ahead and open it manually once you put the disc in. When you have iTunes open the CD that you put in will show up under the DEVICES label on the left hand bar. Select this so it comes up in the main iTunes display. A window will then likely come up and ask you if you want to import the music disc into your iTunes library. Here you can just select yes. It will then go through the process of ripping each song individually from the disc and putting it into your library.
Once all the songs are firmly in your iTunes library you need to put them onto your iPhone. Just go to File and select to sync your iPhone to iTunes again. This will then go through the standard process of syncing, but when you unplug your iPhone from your computer the music files will be added directly to the iPod section of your iPhone.
The great thing about using an actual CD is that you will have less problems with corrupted files and an easier time getting correct track and artist information. Once the songs are in your library you can feel free to alter the information to your preference, including adding album art from the CD. If the CD has an interactive element or extra media on it designed for computer use you are going to have a bit of a more difficult time doing this. Just make sure all of that kind of media is closed out before you begin the iTunes library rip.