Nothing happens immediately --- the regional authorities still have some free space left, although some are planning to get more stingy. (The discussion here --- http://en.wikipedia.org/wiki/IPv4_address_exhaustion --- is at least a starting point for the curious. FWIW, the first that's likely to really run out is APNIC, for the Asia/Pacific region, within the next three to six months; the RIRs for Europe and North America expect to run out in maybe a year or so, and those for Africa and Latin America expect a couple of years' left of run room.)
Once congestion hits (a few months to a year), I think ISPs natting ipv4 clients, or demanding a premium price from anyone who wants a routable address, is likely to happen somewhat more quickly than ipv6 to the home. But that's based on no inside information...