Once you log into Facebook, look for the little padlock icon next to your name on the lefthand side. That's where all the privacy settings are. Click on that, and then click "See More Settings". Next find and click "Ads" on the page that comes up. Then you'll see an "Ads and Friends" section. Click the "edit" link next to that. Here you'll find an example of a Facebook ad, and a drop down menu next to "Pair my social actions with ads for...". Choose "No one" to keep your name from showing up in ads your friends see. Save those settings. There's another "Third Party Sites" section. Click "edit", and select "No one" 'in the drop down menu there also.
Next choose "Security" from the lefthand menu. Turn on "Login Notifications". This will let you know whenever anyone accesses your Facebook account on a new device. Another good thing to turn on is "Login Approvals". This will require a security code that will be sent to your phone whenever you login on a new device. Leo recommends turning on the Code Generator also.
There are more settings you can adjust under "Privacy". This is where you can control who can or cannot see certain posts and personal information.
Remember that Facebook is a free service, so they will use the information that you submit to them for advertising. That's how they make their money. But it's a good idea to ensure that you're protecting yourself as much as possible using the above settings.