Welcome to Android Central! Are you saying that you're putting your music on an external SD card, i.e. one you can remove from the phone? I ask this because phones sometimes refer to the onboard internal storage as "internal SD," and there are plenty of lower-end phones that don't have much internal storage at all. So if you're transferring your music files to "internal SD," you'll probably run out of room quickly on a phone that came with little internal storage.
If you have an external SD card, unmount it from your phone (under Settings/Storage), remove the SD card and put it into your computer. Using your computer, make a folder on the SD called "Music," then copy your selected music files to that folder. Plug the SD card back into your phone, then open your music player--it should automatically scan the SD card for music files. I know that Google Music automatically scans, but if you're using a 3rd party music player, you might have to go to its settings to select other folders to scan.