Iphone/Itunes music transfering

Is there a way to get music onto my iPhone from another iTunes account?
Also, is there a way to put the music from my iPhone onto an iTunes account?
I have new music on my iTunes account but can't seem to find a way to put it on my phone.

If you mean, can you put music from a friends account on your phone? Or put music from your phone onto their iTunes account? Only if you both burn a CD for each other and you load it into the computers iTunes account.

You can have more than one account on the same library in your own house. My sons and I share a library, but have diffnt Apple IDs. We use playlists to keep music we like separate from music we don't and sync only our playlist

You can't sync your iPhone with more than 1 computer. If you sync with another computer you will lose all the content on your iPhone.
If you have music in your iTunes account, all you have to do is;
Plug phone into your computer
Click on the device button on top right of screen
Click on your phone. This will show a Summary page.
Click on music tab
Click on Sync music and check the boxes you want. (Entire library, selected songs or playlist)
Click on Apply button on bottom right
Click on sync.

You can do all the tabs before you click on Apply and sync.