First, make sure you have enough free space on your iPhone to hold the music you intend to place on it.
Open iTunes and decide on which music you wish to transfer to your iPhone. Compile that music into a playlist. Attach your iPhone to your iMac and then sync the playlist you compiled to your iPhone. Note.. any music already on your iPhone will be replaced by what you synced.
Hello - please provide some more information: 1) What iPhone model do you use; 2) What iOS is installed on the phone; 3) Are you using iTunes on a Mac or PC; and 4) Is your music library in iTunes?
I'm going to assume that you have a 'music library' in iTunes on a computer (not sure which one?) Do you already have music on your phone? If not, then a 'sync' as suggested will get all of the music onto your iDevice - but do you already have music on the phone that you do not want to delete - we need to know?
I've been putting music on an old iPod, a sold iPad 2, an iPad Air 2 (my new device), and my wife's iPhone 6 from her iMac - I DO NOT use automatic sync in iTunes (an oft confusing feature when dealing w/ music & photos) - see the first screen capture below - the feature to sync music is 'turned off' because of the confusion of syncing and deleting your music already on the device.
Instead, I like to first add music to my iTunes library, then put together a playlist on the computer, and finlly plug in my iDevice (now an Air 2) - then simply drag the playlists to my device (see the 2nd image w/ the arrow) - bottom line, I'm not deleting my previous music but adding additional playlists as desired (the latter can be one album, several, or a selection of songs) - NOT saying this is what you should do, but simply an alternative that works for me w/o being 'in fear' of this syncing issue in iTunes - Dave