This is all very easy to do and use.
Situation 1: If you have music files ON your mobile device (phone or Pad) you connect the device and Echo's Bluetooth (BT) together. When connected, you start playing iTunes music on device app, and instead of sound coming out the device's speaker it will come from Echo speaker.
Situation 2: Requires a home network be setup and working. Setup properly, an app on iOS device that can access your home network will be able to access your media server device (such as a computer, shared drive, NAS, etc) can be accessed e.g. by Phone and play the music stored on the remote device on phone. From playing on the phone to Echo requires the two to be connected via BT as described abov.
Basically, if your phone/pad can play music on it from any source, it can play it to Echo via BT.
Situation 3: You can also play directly from computer to Echo via BT. Turn on BT of computer, locate the Echo device within the computer BT program, pair the two, and start playing music from computer to Echo!
Situation 4: There is one app for iOS I know of and sometimes use, that does not need a home network setup completely. It detects all the media server devices (via DLNA) on your current network that are turned on and allows you to access it and its folders and beam/fling/cast the music to your phone/tablet, and TV. Your computer will be detected since it is a media server device (at least a Window PC is; not sure about Macs). I would suggest not trying this setup initiall -- the other methods above are easier to use for a novice. The free app is at the App store and is called Belkin MediaPlay.
Using any of these methods ,I can play music from any device or drive in my home to any device I want to, incl. Echo, phone/tablet, BT speaker, TV, etc., etc.
Good luck.