There are multiple ways to sync music between your computer and your phone running Windows 8.1 or 10.
Sync with OneDrive
If you are logged in with the same MS account both into your PC and phone, you can simply drag & drop files into your OneDrive Music folder. All of your files will be available in Groove. (By default it will stream the music, but you can download all synced tracks with one tap.)
- files synced in OneDrive are also available in the Groove Web Player.
- files deleted from OneDrive won't be deleted from your phone.
- this is likely the most easiest way.
Copy files from PC to the phone when it's connected
When you connect your phone with the USB cable it will be in file-transfer mode by default. You can open your phone storage with the File Explorer and copy your music from your PC to the phone's Music folder.
- The phone needs to be unlocked to allows file transfer.
- If the phone gets locked during copy, it will stop the file transfer.
Download the music to your phone and copy it to the music folder
Windows Mobile 10 includes a file explorer by default, for Windows Phone 8.1 you can download one created by Microsoft. Once you have a file explorer you can simply download any music to your phone, then copy it from the Downloads folder into the Music folder.
- On WP8.1 your phone will open music files in the music player to stream it by default. (You can download it from there somehow. I already have W10M, so I can't check.)