There are multiple ways to do that.
Use the PianoTrax App. It's free. Get it at the Apple app store
or Google Play
. Mp3s purchased on the PianoTrax website will immediately be playable in the "My Trax" folder on the PianoTrax app.
Download the Mp3s to your computer, then open iTunes / File / Import. Sync your computer with your mobile device.
Download the Mp3s to your computer, then open Dropbox on your computer and add them to a folder. Download the Dropbox app to your mobile device and find that shared folder. Be sure to "make your file available offline" so you don't need WiFi or cell reception to play it.
Download the Mp3s to your computer, then email them to your mobile device. You can play them from the mail program.
Download the Mp3s to your computer. Email the Mp3 to your mobile device. Tap on them to de-compress the attachment/s. Hold on the icon and a menu will appear to move the file/s to various places like Messages, Google Drive or Dropbox. I know this works on an iPhone, other devices have not been tested.
The PianoTrax app is probably the easiest way to instantly hear your songs on your mobile device.