Be paranoid! When you visit a website for the first time, it can learn a lot about you. If you have cookies on your computer from one of the site’s partners, it can see what else you have been doing. And it can place cookies onto your computer so it can track your future activities.
Many (or most?) browsers have some variation of “private” browsing mode. In that mode, websites shouldn’t be able to read cookies stored on your computer, and they shouldn’t be able to place permanent cookies onto your computer. (They think they can place cookies, but those cookies are deleted at the end of the session.)
Those settings aren’t good enough, because they are either all or nothing, and offer a poor balance between ease-of-use and security/privacy. The industry can and must do better. See why in my essay on NetworkWorld, “We need a better Private Browsing Mode.”