Hi @Ote,
Have you purchased your songs using a streaming service such as Google Play Music? Note that in order to download music to be used offline with these you usually have to do so within the settings of that application.
If you are trying to download songs from a website there is usually a button you need to press to start the download, for example an arrow pointing downwards. If there is no option to start a download, try loading the desktop version of the site. With the website open, press the three dots (if you are using Chrome) and mark the checkbox "Request desktop site". If this is related to the mobile version of this website then this may help.
I'd also recommend that you contact the support for the company that you purchased songs from.
