1 - On PC/MAC/Linux, download the Spotify "App"/Client/program (delete to your preference). Apart from brief samples never listen to Spotify in a web browser. If, as is likely, you pay for Spotify, no matter your browser, music will be streamed at around half the top quality (bitrate) that it will be in its app). It's horrible! Don't do it!
2 - Of course, once you have downloaded the app you will need to go into settings (3 dots, top lefthand corner of the client and then, "edit" and then settings. Here change the "Music Quality" to "Very High" (may read "extreme" depending on Spotify's mood). Note: if you are streaming on a mobile device this will use more of your bandwidth. And while you are in "settings" stay there. You will need to be here for the other recommendation.
3 - In settings, unclick/switch off "Normalise Volume". Seriously, just switch this off. Try a track with it on and then off. If you hear no difference, then fine, but we will be surprised if you don't.
And here are some playlist for you to test out your new settings: