How to sync my own music to my iphone 4s?

Basically, I have music on my laptop from CDs and files that people have sent me,
I've transferred all of them to my itunes library but they are not showing on my iphone after the sync has complete.
Is this because iPhone 4s only allow you to listen to music on it that you have purchased from itunes itself?

ITunes (and iOS devices) are NOT just for music purchased from iTunes.

• Can you see the music in the iTunes Library?
• Does the computer recognize the iPhone and automatically start iTunes?
• Do you see anything strange (messages/errors) as the sync progresses?

If they have been added to your iTunes library correctly, the music from CDs will sync to the iPhone.
it would not surprise me if the files sent to you appear gray, and will not sync to the iPhone or say "not found".
iTunes doesn't allow pirated music. Only legally purchased music. If you have a CD, iTunes assumes you purchased it and allows you to import the CD directly into your iTunes library, usually with all the information intact (song title, artist, etc.)

Once you select your iPhone from the devices (top right button on the iTunes screen)
This should show a summary page with the name of your iPhone.
click on the music tab
check the box that says sync music.
this will allow you to chose all music (library) or selected playlists or songs
click on Apply button on the bottom right
then sync

if you missed any of these steps it would explain why your music isn't on the iPhone