Welcome to Android Central! You have a few options.
1. If you'd like to have access to all of your music via streaming over wifi or 4G, then upload your entire music library to Google Music. You can then access all of your music using the Play Music app. You'll need to install the Google Music Manager on your computer--here's the link:
2. If you'd like to have your music locally available (if you don't always have network availability, or if you need to keep your network data use down), then you can simply transfer your music to your phone, and it can be played by Play Music or any number of music player apps that you can install from the Google Play Store. You can transfer music by connecting your phone to your computer via USB, then drag and drop your music to the Music folder on the phone's internal storage. I suggest using the conventional folder hierarchy of Artist/Album/Song. If you have difficulty with USB transfer, then try wireless transfer by installing . If you'd like to use a different music player, some good ones include PowerAmp, Winamp, MortPlayer, and DoubleTwist, but there are a LOT more available.
3. If you have an Amazon account, you could also upload your music to the Amazon cloud and use the player, but the amount of music you can store for free with Amazon is significantly less than with Google.