How do websites track your activities?

[Jake]

Yea a lot of tracking is done with anonymous cookies set in your browser, that's a little bookmarked information stored under the site name, Amazon might know that you were looking at chairs but would not know your name. Ad re-targeting, the practice of showing banner ad reminders about some product you recently looked into is a quite common and has been proven effective. Many such banners have a triangle Adchoice symbol that accesses options allowing you to opt out of the advertising campaign.
You can also clear the cookies in your browser preferences, though this deletes useful shortcut information for some sites you use, better to look at the cookie list and delete those you don't recognize.

If you click a link to access a site the new site can tell where you just came from, if you use a search engines it also knows the search keyword used to find them.

Generally speaking if you have not created an account with a web site they only know you by your unique internet IP address, some connections like DSL can change the IP each time your modem reconnects. They can estimate your city based on the IP address.