iTunes; how to move songs to iPhone?

[Iphone4sinwhite]

I recently "add to library" some songs from a CD to iTunes. I'd like to move these songs to my iPhone. I've connected my iPhone via USB to my Mac but it won't let me drag and drop the songs from iTunes to the iPhone, the songs just bounce back. Also, when I click on the music already on my iPhone they are greyed out and I can't play them in iTunes. I have tried File>Sync iPhone but that hasn't helped. I'm using the latest version of iTunes and 6.0.1 on my iPhone.
Is there anyway I can transfer music to my phone?

[Madmic23]

1. In iTunes, select your iPhone from the Device list on the left. This will bring up your iPhone in your main iTunes window.
2. Use the tabs along the top to pick what you would like to sync, in this case, music.
3. You can either sync all of your music if you have enough space, or you can click "sync only selected songs and playlists" and check off what you would like. This is where you also select photos and movies to sync as well.
4. Click "Apply" and wait for the sync to complete.

Hope that helps. You can use the link below for more detail direct from Apple.
http://support.apple.com/kb/ht1351

[Iphone4sinwhite]

Originally Posted by Madmic23

1. In iTunes, select your iPhone from the Device list on the left. This will bring up your iPhone in your main iTunes window.
2. Use the tabs along the top to pick what you would like to sync, in this case, music.
3. You can either sync all of your music if you have enough space, or you can click "sync only selected songs and playlists" and check off what you would like. This is where you also select photos and movies to sync as well.
4. Click "Apply" and wait for the sync to complete.

Hope that helps. You can use the link below for more detail direct from Apple.
http://support.apple.com/kb/ht1351

Thanks Madmic23! Only some of the music I have on the iPhone right now is shown in the library at the top of the left side of iTunes. When I click iPhone under devices all of the music on the phone is shown (greyed). If I select Sync, will it remove the music I already have on the phone that is not shown in iTunes library?