IPhone 4 and iTunes won't work. Trouble adding the music on my phone?

I have the iPhone 4 and I imported several CD's, downloaded two mixtapes, and bought a few albums and songs and the ones that I bought are fine and are on my iPhone, but the mixtapes and some of the songs on the CD's won't go onto my iPhone. I have hit apply after trying to add them. It didn't work. I put them in a playlist. Still didn't work. It took me a very long time to get these CD's I wanted onto my laptop and would like them on my iPhone. Please help! Very appreciated.

Added (1). I have tried syncing. It still doesn't work. :/

Added (2). I have synced to the computer before. The music plays in iTunes. I have updated iTunes. There isn't an error message.

Try syncing your music library to your phone. It should fix your problem. Then do a full iPhone sync

Does all the music play directly from iTunes on the computer?
Error message? Is iTunes up to date?
Have you synced to this computer before?