Step -1: We started running out of IPv4 addresses. The internet is IPv4-only for all practical purposes. Nobody is doing IPv6 because it's still experimental. Your weird neck-bearded friends are talking about it, that's about it.
Step 0: Inception! IPv6 is now a standard and you can route IPv6 over the tubes. Two networks have connected!
Step 1: Dual stack is a thing. Now you can set up both IPv4 and IPv6 on the same network and they co-exist. Some hosts (goole.com, facebook.com) try this and finally turn it on for good in 2012.
Step 2: Dual stack intensifies. This is where we are now. You cannot yet run a full blown IPv6-only network that you want to talk to the Internet and do anything practical with it, but all your cleanly shaven friends are now telling you that you should support IPv6 first, then add IPv4 for compatibility. Google sees as much as 3.5% of their traffic over IPv6.
Step 3: The cost of any single IPv4 address rises dramatically. For an end user it's already roughly $1/month. Buying in bulk is much cheaper, but not free like it used to be. ISP's and other service providers (Amazon, Rackspace, Digital Ocean) are going to start noticing the costs on their bottom lines. Severe restrictions are imposed by IPS's and service providers on anything but the bare minimum of IPv4 usage.
Step 4: The future. The first IPv6-only networks start to pop up. They use special network translation to talk to IPv4-only internet. (You can do this at home now! It's called NAT64: http://www.litech.org/tayga/).
Step 5. The number of IPv6-only networks is growing rapidly. IPv4 is now a legacy protocol. All your friends are telling you that they cannot believe we are still using IPv4 and how much of a pain it is to support it. Sales of T-shirts with "There is no place like 127.0.0.1" drop dramatically.
Step 6. The same people that put together IPv6 World Launch Day put together an IPv4 funeral. Major companies turn off IPv4 presence.
The crucial point here is not that someone demands IPv6 by calling their ISP, etc. It is fun to play with and you should at least get a tunnel set up through Hurricane Electric if you are reading this, but the demand here does not matter. What matters is supply: supply of IPv4 that is. Once that goes to nil, the cost rises and some executive at every ISP and service provider has a bright idea to save the company millions by switching everyone to IPv6. That's it. We, the people in the trenches, cannot affect this. We cannot speed it up and we cannot slow it down. The invisible hand of the market will make IPv6 happen all on its own.