It's possible, but complicated -- here's the basics:
1. Login to Facebook and click the "Account" button on top right hand side
2. Select "Privacy Settings" from the drop down list
3. Click the "View Settings" link under the "Connecting on Facebook" section at the top
4. The first page allows you to choose who can search for you, send you messages or connect. Set each of these to "Friends Only", then click the "Back to Privacy" button at the top.
5. Next, select the "Customize Settings" link at the bottom of the "Sharing on Facebook" section. Make sure ALL of these settings are set to "Only Me". This means you will be the only one to see these things. Don't miss the "Things others share" section, where you can prevent your friends from checking you in or writing on your wall. Click the "Back to Privacy" button when you're done.
6. Scoll to the bottom left under "Apps and Websites" and click the "Edit your settings" link. This controls how apps can use and access your profile. This page is GIANT (if you've used Facebook to login to other sites or installed any apps). Remove andy app or website you don't want to have access to your data. Click back to Apps. Next click "Edit Settings" in the Instant Personalization section. Uncheck the box. Then click back to Apps. Finally click the "Edit Settings" next to the Public search section. Uncheck the box. Click back to Apps. Click back to Privacy.