Being more specific, I would like to know which are the possibilities for a webbsite owner to detect whether the same user logs with different accounts, and how to bypass each of them. For example, I already know coockies and I guess it is enough to use the private browsing function of the browser, and to be sure to carry out temporary files removal with some program as CCleaner. That is my first question so I hope it is everything correct. I apologize whether actually it is not. Thanks in advance for every answer and suggestion.
You could use browser fingerprinting, most browsers are unique in the plugins they use, version of those plugins, screen resolution (if you use your browser in full size) etc.
You can check your browser fingerprint here