The way that you experience mp3 downloads will depend on your setup - e.g. whether you are on a PC or Mac, and which operating system and browser you are using.
In many cases clicking with the left button on the download link or icon will play the file. Clicking with the right button on the link or icon should display a list of options. One of these options is likely to be "Save Target As..." or "Save Link As...". If you select this option (or any similar option containing the word "Save") then you should be able to save the mp3 to your computer.