On Web, you can download tracks once you have signed in to your SoundCloud account by clicking on the download file button beneath the waveform: 

You can enable, or disable downloads for your listeners through your track's Permissions tab. Enabling downloads means that your listener can have a copy of your original file format that you have uploaded to SoundCloud. 

Please note: Not all tracks are downloadable. If you don't see a download file button, it means the user who uploaded it did not intend for it to be downloadable. Additionally, only individual tracks can be downloaded and playlists as a whole are not available.

Saving content on mobile devices

It is not possible to download a track from a mobile device. However, users with a SoundCloud Go or Go+ subscription can save content for offline listening on a mobile device.