Cookies and/or Local Storage
My site uses two basic cookies - one to show that you've seen the cookie disclaimer, and one to store your stylesheet choice. Both of these are stored on *your* device, and not on this site.
Other than that, I store nothing about my sites visitors, aside from the basic statistics that my webhost saves. I have little to no control over that, sorry.
I may make further use of cookies in the future - or, possibly, localStorage - for the tools section as I implement them, but you can always view what (if anything) a website stores in your browser.
You can view that data in Firefox simply by pressing F12 while on a site, clicking "Storage", and exploring the sections shown.
Alternately, you can look for info online on how to view this data - like this site.