"The Process". Sounds like a John Grisham novel right?
Anyways, so here is the process:
1. Be self-aware
Know what you bring to the table before you start talking to people.
2. Refine a pitch
When you starting talking to people, you should have a brief/impactful way of introducing yourselves.
3. Know what you want to know
Have an idea of why you are networking. Don't get on to the phone and ask for a job. Try to find out about field, genuinely and sincerely. Jobs come and go, knowledge has to be invited home.
Talk to as many VCs as you can and get in front of them with your ambitions in tow.
5. Do a field study in a VC related topic
Try to do a field study in a VC related topic preferably with a VC firm and get a hold on the street lingo in VC land. ("Carry" is not a verb as much as a noun in a VC song and things like that).
Refine your idea of what you bring to the table and what kind of VC job you want, and use that to talk to more VCs.
7. Subscribe to tech/VC blogs
Ensure that you are on top of the tech startup world/trends by subscribing to influential, interesting VC/tech blogs.
8. And network a bit more
Keep talking to as many people as you can. Essentially, when the right position comes by, someone should remember you. That is the only way one gets a job in VCland.
(Unless you are Ankur Luthra (Summit Partners) who got his pic in Wired magazine gazing at a wall full of business plans)