Facebook helps you connect with people you may know by automatically suggesting friends on your home page. Facebook bases these suggestions on many factors, including your existing friends, your schools and your company. Because the feature is automatic, you can't turn it off, but you can modify who can receive you as a friend suggestion and block people you know you don't want to be Facebook friends with.
If Facebook suggests a person you don't know or don't want to be friends with, click the "X" at the top-right of her information box. Her information box will disappear, and Facebook will not suggest that person for you again.
If you don't want a person to see your profile and don't want to see his profile, block him from your account. Go to the "Account" menu on the top-right of your Facebook page and choose "Privacy Settings." Find "Block Lists" in the middle of the page then select "Edit Your Lists." Enter the person's name then click "Block." He will not be notified that you blocked him, but he won't be able to search for your profile. Also, Facebook will never include him in your friend suggestions, or you in his suggestions.
Lower Your Visibility
The fewer Facebook friends you have, the less likely you are to receive friend suggestions. Lower your visibility to limit how many people you are suggested to, as well as how many people will appear in your suggestions -- this will create a smaller pool of potential suggestions, and once you block a suggestion, Facebook won't revisit the connection. Go to your "Account" menu then select "Privacy Settings." In the "Connecting on Facebook" section, choose "View Settings." Change the setting for those who can "Send You Friend Requests" to "Friends of Friends" instead of "Everyone."
Facebook's Friend Finder allows you to upload contacts from your e-mail accounts, and invite some of them to be your friend on Facebook, or create a new Facebook account. Once you use this feature, Facebook my begin offering friend suggestions based on people who have your e-mail address in their contacts. To stop this, remove your contacts by going to your "Account" menu then to the "Help Center." In the top search field, search for "Remove Imported Contacts." Click "Remove."