How to sync my songs onto my iPhone?

When I go onto iTunes its says you have the option to sync only checked songs, but when I go to sync the songs I checked they won't download onto my iPhone. Anyone have any suggestions?

Are they greyed out on the computer?

Are you sure you have authorized the computer to download to your device? Click on your email address at the top of the page in the itunes store and select 'your account' look in here and ensure
your computer is authorized.

This may be the issue, if not edit back for further assistance.

I don't know if you have updated to the latest version of iTunes yet, because the interface has changed a bit. Plug your phone into your computer. After a few moments, if you have the old iTunes, you will see the icon for your phone pop up on the left. Now, just select the songs you want from your library, and drag and drop them onto the phone icon. In the new iTunes, once you select your songs and begin to drag them, a panel will pop out on the right and you should see the icon for your phone there, and then you will just drag and drop again. Hope that helps.