How to transfer songs from iTunes to non synced iPhone?

So I transferred some songs from a hard drive on to my iTunes and I can't seem to put them on my new non synced iPhone. I've tried to drag and drop them and nothing seems to happen. I've also tried to transfer the file itself from my computer to my iPhone, but then it tells me that my device is not responding. All of my software is up to date and all the songs I transferred will play on the iTunes but I just can't seem to get them on to my phone.

Added (1). Well I got a bunch of stuff on it that I don't want to get rid of so I'm sort of looking towards not syncing it but just getting the music from the iTunes.

You have to get iTunes to recognize the iPhone to sync it.

Well in your case,
You can't copy your music to your iPhone without using the itunes.

also You can manage your music manually in iTunes.

if you need just to sync some songs not all your library, you can create a new playlist, and add all songs that you need to put in your new iPhone, then, Plug in your new iphone then open itunes, and click on your iphone.
On the summary page, look at the end of it, you'll see a box named Options.
under Options look for " Manually manage music and videos. "

then go to Music tab, and check the Sync Music,
under it, there will be two options,
select "Selected playlists, artists, albums, and genres".
Then you can just check your playlist that you already made, and click sync.

This way it will only sync the selected songs.