Drag and drop, I'm amazed that people use auto-sync personally.
Really, you don't use Smart Playlists? I love them. I've got one that copies 25 random songs from my library that have never been played, another one that keeps my favorite songs synced, another one that keeps 25 of my favorite songs that I haven't heard in the last month, another one that keeps the last 50 songs added to my library, etc. The songs automatically change on those based on last play date, ratings, date added to library, etc.
I couldn't imagine managing music manually. I guess if your library is small enough to fit entirely on your device, that'd be OK.
I am looking to drag and drop music to iPhone instead syncing. When I click on Manually manage music in iTunes, it wants to erase and sync But then I'll lose what's on iPhone. Could you please tell me how and fro where to drag and drop?
AFAIK, you can't do what you're trying to do.
If your iTunes is telling you that, it's because it thinks those songs on your iPhone came from a different iTunes library.
You can buy a program like senuti which will copy the songs on your iPhone over to your computer, then you can erase and sync everything back.
But in general, no, you can't just hook up to some random computer and transfer new music over, at least not with the Apple "Music" app in iOS + iTunes.