The explosion of the internet has changed the rules of the game with regards to networking. While it has provided us with a lot of avenues, the process of contacting someone in your school network should not be considered a free for all. People who are prudent and forthright can make successful connections, but those who show poor judgment might alienate themselves quickly.
Generally, universities will have a directory of staff and students that lists contact info. When reaching out to someone, appropriate ways to contact someone is through e-mail or phone. Sending a letter is fine, but computer use has become so commonplace that an e-mail is perfectly acceptable.
An e-mail should be respectful and honest. You should introduce yourself and explain why you are contacting this person. Refrain from getting too personal and write the e-mail in letter form. Granted, not all e-mails need to be grandiosely formal, especially when you're addressing a peer. The greeting, body and closing with your signature should be sufficient. It's also important to include your own contact info.
The boom of social media has turned Facebook into a networking machine. Pretty much everyone has an account on facebook these days, making it fairly easy to get in touch with a schoolmate. After you do a search and locate an individual's profile page, contact that person by sending a private message. Like an e-mail or voice mail, this allows you to introduce yourself. Trying to 'friend' a person right off the bat can be a little forward.
Facebook is particularly effective since it organizes your network by schools. Unless a person's profile is blocked, you are allowed to view other students that attend your school. Social media does have its stigmas, though. Avoid being ignored by declaring your purpose. It's also advisable to state how you heard about an individual. It never hurts to say, "Hello, my friend informed me that you work for such and such company." Just be sincere and polite.