Facebook users can choose to provide an email address on their About page, so if you are looking for an email address, this is the best place to look. However, listing an email address isn't mandatory.
How to Find an Email Address
Log in to Facebook and go to someone's profile page. Click the About tab below the Cover photo and click the Contact and Basic Info option. If your friend wants people to contact her via email, her Facebook email address displays in the Facebook section under Contact Information. When you send a message to this address, it's automatically forwarded to her email address.
Some people may include an email address in another field. In the example shown here, this person has an email address inserted in the Address section at the top. He has also included a Twitter account address and a website, which can be used to contact him.
Friends Who Haven't Provided an Email Address
If you are friends with someone on Facebook who hasn't listed an email address, you can ask her to provide one. In the Email section of the Contact Information, click the Ask for (friend)'s Email. Your friend will get a message from Facebook with your name, stating that you are asking for her email address. While this option doesn't give you the opportunity to type a message, it does tell your friend that you want to send her an email.
People Who Aren't Facebook Friends
If a Facebook user has made her contact information public to everyone, the email address appears in the Contact Information section, even if you aren't friends. However, if that person has opted to keep the information private, or hasn't posted it at all, no email field appears on the About page, not even a link to ask for an email address.