Connect your phone to your computer, when it appears on the left sidebar of iTunes click on its name, then check the following:
- On the summary tab to the right you have checked "Sync only checked songs and videos" and you have not checked "Manually manage music and videos"
- On the Music tab to the right you have checked "Sync Music"
- Click on Music under Library on the top left and make sure you have checked the boxes to the left of all the songs you want to sync to your phone
- Confirm that there are no exclamation points next to any of the songs you want to sync to your phone
- You have authorized your computer for all Apple IDs for purchased music you want to sync to your phone (in Store>Authorize this computer)
When everything looks correct, click on the name of your phone again and tap the Sync button on the bottom right to sync your phone.