The number of IPv4 addresses used on the Internet is limited, IANA the organization in charge of the addresses allocation has assigned the last ones during the beginning of 2011.
In 1990, the end of IPv4 was predicted for 1994. The abandon of classes based addressing and the wide use of NAT brought IPv4 until now. IPv6 was developed by the IETF to succeed to IPv4 and in 1996 the 6bone, the first IPv6 network, was ready for testing IPv6. Linux and some Free software where also ready at that time. Six year later, service pack 1 brought IPv6 to Windows XP.
The immediate benefits are poor: nobody use IPv6 these days and most of the lack of IPv4 are already covered by extra protocols. IPv6 is more seen as a problem than a solution.
Even if both protocol can share the same infrastructure and applications require only limited changes to handle IPv6 addresses, the two networks are distinct and computers cannot communicate when mixing both protocols. Some higher protocol like SMTP for mail or HTTP for web already handle proxy features. A proxy can be used as a gateway between the two protocol and let IPv4 and IPv6 host inter-operate through this higher protocol. But a proxy is an expensive solution that require powerful hardware and lot of maintenance ! The best solution for a host to communicate with both world is to have a dual IP stack, one for each network. This is to the application to know witch stack (or address) to use when opening a connection. All IPv6 ready OS and applications already support the dual stack.
The lack of addresses don't like to alarm anybody. Most of the ISP are discrete about IPv6 and few of them provide IPv6 connectivity. The first reason is probably the lack of requests from the customers. Anyway they must have a plan for when they are out of stock !
If you move to a new home or a new office in the future, or if you buy a new host on the internet to host a WEB site or any new service, it is possible that you get no IPv4 address ! At least your ISP or hoster will give you an IPv6 range with billions of addresses, and, because IPv6 addresses are still mostly useless, a private IPv4 address behind a router doing NAT to give you a kind of restricted internet access. When your are behind NAT, everything that was requiring port forwarding on your own router or firewall become unavailable, at least through IPv4 ! To overcome these limits, your ISP will probably give you plasters for most common need. This is at price of some complexity increase. I think this situation could last for some time ....
The IPv6 community will grow continuously and become more and more financially attractive. More and more Internet services will become available through IPv6 and one day IPv6 community will overtake the IPv4 one. That day the IPv4 will be left behind. This is the day where you will have to switch yourself !
Another script include an application that would take advantage of the new IPv6 features. To take benefit of the these advantages all users of the application would have to switch to IPv6. If this is related to a very popular service like Google, Gmail, Youtube or Facebook, a lot of user could be interested and the switch could be considerably faster !
None of these 2 possibilities will imply the end of IPv4, but the extra cost for maintaining both addresses will quickly kill IPv4. Anyway IPv4 could still exist for decades !
I don't thing you have to take care about IPv6 until others, at least ISP, start to communicate around it. In any ways, it is not in your interest to leave IPv4 too early. If you renew your Network infrastructure in next years then be sure all the devices are IPv6 ready.