How to get the songs that I want (and only those songs) on my iPhone 4S?

I was originally having problems with iMessage, and decided to try restoring my iPhone 4S. After restoring, erasing all contents, and then restoring from backup, every single song in my iTunes is appearing with the iCloud symbol on my iPhone, even if they are unchecked, and even if iCloud is turned off. I have turned off iTunes Match and tried restarting both my computer and my iPhone, but nothing seems to be working. Any help would be greatly appreciated.

Just open itunes and then copy the song from your hard drive then go to itunes and click on edit and then paste