There is a lot to learn in order to protect your privacy online.
Use a search engine to search your name and you might find plenty of websites that troll data like whitepages, land records, and voting records and put your information online. To protect your privacy you need to visit each of these sites and opt-out. How-to opt-out of people search websites
Google search has an images page that you might want to search your name on. Another interesting feature is search by image. Go to Google Image Search and click on the camera icon. From there you can upload an image or use a webpage address of an image and Google will compare it with similar images. Before you give Google any information about yourself you may want to read the rest of this page first.
Firefox and Chrome both have addons that let you block ads, tracking cookies, and annoying social media icons on webpages. Preventing these things from downloading will not only speed up your download times but will protect your privacy.
AdBlock Plus used to be the addon to use but then they started allowing ads for companies who paid them to whitelist their ads. So a complete adblocking addon was created called Adblock Edge
Once you install it I recommend adding these filters to it: Fanboy Ultimate Adblock list (This includes Easylist, Easyprivacy, Enhanced Trackers List (like Google analytics, and Annoyances List which includes social icons)
When you use messaging in Facebook it sends a notification to the other user(s) in a conversation that you've "Seen" their message. You can prevent this using adblock by adding this filter: /ajax/mercury/change_read_status.php$domain=facebook.com
Sites can not only use browser cookies to track you but they can save cookies in Flash if you have that plugin. Better Privacy is a Firefox addon that clears the Flash plugin's cookies when you close your browser.
Any website can see your IP address because it is necessary to have your address in order to know where to send a response once you request a page from a website. There are websites that let you map an IP address to a general physical location (GeoIP). Here is an example. Headers are information sent between your browser and a website that you might not be aware of. Headers can contain information that affects your privacy. Some of those headers are: cookie, referrer, and user-agent. There is also a "do not track" header that was supposed to allow you to opt-out of being tracked by a website but in reality it is used as another piece of information that can be used to identify you. Many things can be used to identify you such as your IP address, your browser's user-agent (name and version), what plugins you have installed or do not have installed (Flash (and Flash Local shared objects, i.e. Flash cookies), Java, etc), what extensions you have installed (adblock, etc), and even what fonts you have installed.
Turn off the referrer header in Firefox. When you click on a link that takes you to a different website, a HTTP header is sent to that site with the address of the site you were just on. Turn this browser feature off to protect your privacy.
If a website has set a cookie in your browser then each time you visit a page on that website your browser will send that "cookie" header to the website. Usually a cookie just consists of a unique identifier that is set when you login to a website that requires a username and password. That way the website can verify that you have an active session without requiring your login credentials for each page of the site. Note that you should never use an unencrypted wifi network to access any websites that require logins because someone sitting near by may be sniffing your network traffic out of the air and be able to make a copy of your cookie, thus allowing them into your account. Most websites have a secure login (https) which encrypts the data going between you and the website to prevent this but sometimes the website does not use https for the rest of the site which means your cookie could be copied. Even an image on a website that is not requested over https instead of http is an open hole. That is why browsers show messages like these sometimes: "You have requested an encrypted page that contains some unencrypted information"
Your browser also sends a header known as the user-agent to websites containing the browser name and version. You can make your browser seem like it is a different browser. Note that there are some things websites can do to check if your browser is actually what it says it is and they mostly involve supported or unsupported features or bugs that the websites can test for. You can change your browser's user-agent string if you like but some sites may render differently based on the user-agent. For example if you changed it to a mobile browser's user-agent. Changing your user-agent might also make you more identifiable if you changed it to something non-standard like "no info for you!" To change it in Firefox type about:config in the address bar. Then search for "useragent" and if "general.useragent.override" does not exist yet, right click and select "New -> String" and enter it as the string name. Then change the value to whatever you want.
Use DuckDuckGo as your search engine instead of Google. They do not send referrer headers or your search terms along to the sites in their search like other search engines do. They also do not store your searches, IP address, user-agent, or cookies to protect your privacy.
Windows tests your internet connectivity by periodically attempting to connect to one of Microsoft's servers. Protect your privacy and turn off the Windows Network Connectivity Status Indicator dns.msftncsi.com (126.96.36.199) HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\NlaSvc\Parameters\Internet Under the Internet key, double-click EnableActiveProbing, and then in Value data, type: 0