On the iPhone summary screen you have two options. Sync specific albums by music tab or you can sync all but let the iTunes main library sync checked specific songs. To do the latter:
- on the iTunes, go to iPhone summary screen
- check the box "sync checked songs and videos"
- on the music tab of the summary, select all songs. Same for the rest of your tabs. Apply.
- on iTunes main under your music, check what songs you want to sync. Even videos.
- on the iPhone summary screen hit sync.
I can move the songs onto my phone now, but when I look at the phone's menu on iTunes it is still showing "phantom songs" that aren't on the phone amd are gray. THe hae a sync symbol to the left of each song. Some of the songs are showing up as on my phone and are shown in black with the grayed song underneath it.