LegalJob was relayed a networking story in which the aspiring associate was told from the person he was networking with that xyz firm is not hiring but he will keep the associate posted and to let the partner know if there is anything he can do in the meantime (because he is, of course, happy to help as are many people). The aspiring associate left that meeting with no prospects. What?!
That offer is a great opening! ALL people can be helpful to you in this process by connecting you with one or two other people whom they think may be helpful. It's best when that person reaches out to his or her contact directly and introduces you (so request that) but self introductions (based on that person's recommendation) can also work.
Every contact is an opportunity to generate additional contacts. If you have this mindset, you should be getting some hits after meeting the fifth person or so down the list. You can help yourself even further by doing some research about who your initial contact may know that can be helpful to you (including folks at firms you are targeting) and then you can ask to be connected to that person or person(s), regardless of whether the new person is looking for people. Now is not the time to be shy. The worst that can happen is that the person refuses to connect you or flakes out after your meeting (more likely). There is not much risk in asking. Sure, you could annoy someone you met with who one day may have a job opportunity for you but that is not very likely. DO NOT WAIT TO BE CONNECTED TO PERSON WHO IS IN A POSITION TO HIRE. You never know. For the right candidate perhaps a firm can find an opening.
Make every meeting count by having as a goal to obtain one or two names of useful contacts. In this way anyone can be helpful to you in this process whether or not they are at a firm that is hiring.
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