In short, you should contact everyone you know (your 250, as described below) and everyone you do not know personally, but who may be able to help with your job search. I realize that seems rather open-ended, so let's start with some specifics.
First, contact your relatives. Not just your immediate family—branch out into the family tree. And not just those who are well-connected in business. Your Aunt Mabel might play bridge with someone who knows someone who is a Hiring Manager in your field. Remember, it's not necessarily who you know, but who they know.
Next, contact friends. Old and new, high school and college, neighbors and social acquaintances. They might even be a friend of a friend or relative, such as someone who plays tennis or golf with your parents. Spread the word. Some of the best contacts in this category are your college friends who graduated last year. They have already completed the job search process and probably have lots of fresh contacts and free advice.
Then, contact every known entity within your college. Professors, advisors, administrators, counselors, coaches (they are often amazingly well connected!), and anyone else who has ties to your school. Some professors are very well connected through either industry research projects or direct consulting with employers tied to the academic major. Although beware that some professors, especially some of the "academic purist" or "research first" professors, are not nearly as well connected with the real world as they would like you to think. Yet the guilt factor—not wanting to admit this little secret—often pushes them to come up with some creative ideas. And be sure to reach beyond your circle of known alums to all alumni (recent or past) who are working for target companies, within your target geography, or within your chosen profession. Spend an afternoon at the campus Alumni Affairs office. This office is dedicated to networking with alums. They are usually more than willing to help, since you will soon be an alumnus as well. And you can't pay your alumni dues without getting a job first.
Also contact past and present employers, coworkers, professional associations, and social contacts through your church, synagogue, club, or other organizations. Make it your goal to reach out to your entire list of 250 and then some.
The Law of 250 states that every person knows at least 250 other people. For example, if you were to make a list of people to invite to your wedding, you would likely be able to come up with about 250 people. A corollary is that you likely have 150-200 truly close friends on Facebook (not just Friends as Facebook defines them, but people you truly know well). Then there are another 50-100 you are not connected with on Facebook, getting you again to 250.
On first review, these people may not appear to be outstanding first-level job networking contacts, yet many will be able to refer you to others who are.
Expanding the concept of the Law of 250 further, each one of your contacts knows an additional 250 people. Yes, there will be some overlap in the 250, especially with a family member or close friend. But the exponential multiplying factor of the additional contacts is what makes networking so potentially valuable in your job search.
Use the Law of 250 as continual inspiration to contact one more person to enter into your personal network. Although you may not find your next job within your 250, it is very likely that it may exist within someone else's 250.
A corollary to the Law of 250 is the strength of weak ties. As we stated earlier, if one of your 250 is also a family member or close friend, there will be some overlap. You may have fifty, one hundred, or even one hundred fifty contacts in common. So actually it is those who are the weakest ties who have the greatest potential for your network. Your weekend tennis partner may share no first-level contacts within your 250, potentially opening you up to an entirely new group of people.
It is typically not your first-level contact who will be your eventual Hiring Manager. You will usually find your hiring contact two or three levels deep in your network, possibly even deeper.
This is not to discount the importance of the first-level contacts—they are the starting point and will determine your eventual success or failure in networking. But don't be surprised if one day you get a call from a person completely unknown to you—a "friend of a friend of a friend" referring you to a particular company. Cultivate all your contacts and watch them grow!
Just like the Six Degrees game, except in this case you only get three degrees of separation instead of six. First of all, let's explain why six degrees of separation works to connect everyone to virtually everyone else: take 250 (your personal network) to the sixth power. I know, it's higher math. But do the calculation. The answer is 244,140,625,000,000. That's over 244 trillion potential contacts in your network at the sixth level of separation. And that's how Kevin Bacon can connect with the Pope.
As we talked about in The Strength of Weak Ties, the actual number of potential contacts is reduced by overlap. But the formula is still a strong one—the greater the number of levels of separation, the more likely that your network will include your eventual target.
So if you have a specific contact or an employer you would like to target, use your network to reach out to up to three degrees of separation to make a connection. Why three? Because the network connections lose strength as the degrees of separation increase. Three is the practical limit for job search. That's also how LinkedIn operates on this networking model, requiring you to be within 2-3 levels to make contact.
Let's take a practical example. Suppose you are interested in working for IBM, but you have no contacts there and they are not recruiting on your campus. Tap into your network, especially those who are professional networkers, such as those in the Career Center or Alumni Office (first degree of separation). They may be able to put you in touch with a previous graduate of your school who works at IBM (second degree of separation). And that person may be able to put you in contact with several Hiring Managers at IBM (third degree of separation).
It's actually quite easy to work your way through the degrees of separation. Just like the game, you will be amazed at the connections that can be made.