How to transfer music from my computer to iPhone?

I just got an iPhone 5. I have a computer full of music on iTunes. But how do I transfer it onto my iPhone? I plugged the wire in but it isn't synching.

Download the latest copy of I-tunes, Install, Plug your I phone in to your computer (after restart), open I-tunes (after plugging in the I phone) and wait, the maximum time you will need to wait should be no more than 20 minutes if you have a slow computer. A fast computer should do it in 4 minutes, you are basically waiting for the computer to detect the I phone as a device and tell I-tunes that it is there.once your I phone appears in I-tunes on the device menu click on it for information about how much space you have available for music transfer. Then go to the music menu in I-tune and select the music you wish to transfer, you can either right click and select send to (xxxxxx = name of I phone) or you can drag the selected music to the I phone.

First you have to allow the iPhone to be on your account. After that, What i do is open the ITunes app on the phone, go to "More," then click "Purchased," then click, "Music," and then you can go from there! Your artists should show up. THat was an alternative way. But make sure your ITunes account is on your phone!