This varies depending on the device. The best option is to use either Dropbox or Google Drive and save the files to these apps on your device.
Mac users: Once the files are on your computer you can add them to iTunes and then sync your iPad or iPhone to iTunes.
Windows/Android users: Connect your mobile device via USB to your computer. Locate the downloaded files on your computer and transfer the mp3 files to the music folder on your mobile device. This is usually a simple drag-and-drop operation.