By default a user can save any image by right clicking on it in their browser and selecting “Save Image…” or similar.
HTML5 offers a download attribute to the <a> element that will attempt to force the browser to download the image. So your resulting HTML would look like this:
<a href="https://wordpress.stackexchange.com/questions/293568/{{ url of image }}" download>
<img src="https://wordpress.stackexchange.com/questions/293568/{{ url of image }}" alt="Alternate Description for Assistive Technologies" width="700" height="320">
</a>
Additionally, the download attribute can take a file name too so download becomes download="SaveFileName.jpg"
Without knowing more about how you want to do this, I cannot offer up any WordPress code.