Some information you choose to put out on the web on purpose, so that you can share it with others. Great. Some information gets put up by others about you by your family, your friends, or your school. Maybe great, maybe not, but there it is nonetheless.
How much of what is out there do you want to share and with whom?
There are three different aspects when considering web privacy:
Much of what you do on the web is trackable. Your computer has a unique address (the IP number) that connects your computer specifically to the activity you engage in. This is mainly done through server logs and cookies, but if you are logged into an account somewhere, like a web-based e-mail account, then that company can track you in additional ways.
You may or may not care, but you should at least know what's going on so you can decide what to do.
Server Logs: These are automatic, and from a user perspective, not much can be done about them. The technical issues of changing them on your own computer are beyond the scope of this tutorial, but know that they exist and can provide a listing of activities done by that computer. And the user can't do anything about server logs on other computers that they connect to through the web.
Cookies: These are little bits of information placed on your computer by websites to remember you. If you have automatic log-ins to certain sites, that is likely done through a cookie. There are privacy settings in a web browser like Firefox and Internet Explorer that let you restrict these if you like. Restricting them can have some impact on how things work (like letting a site remember what is in your shopping cart).
Caches and web history: These are logs of which sites you have visited in the past. They can usually be managed within a web browser; both Firefox and Internet Explorer have options for clearing or restricting history and for setting the browser for private browsing.
Who's tracking what and how can you stop them? Search engines are tracking you, advertising companies are tracking you, and any web site you've visited who has the right kind of cookie can track you. Restricting this kind of tracking usually means a combination of setting your browser to minimalist levels and explicitly setting your accounts and privacy options wherever you can. You may or may not think it is worth it, but you should know that you can adjust some account settings if you care.
Google does have a few places where you can adjust your personal settings. Some go with the computer (IP address based), some go with the browser (but may require you to download Chrome - Google's browser), and some go with your Google Account. The three most relevant places to look are: