The Internet is many things: good and bad (and worse) business models, techno-libertarian governance and state censors, information and misinformation, empowerment and addiction. But at heart it is the machine with the most parts ever created. What I've learned from the Internet comes not from Web 2.0 or anything else.0, it's the original insights from the pioneers that made its spectacular growth possible.
One is interoperability. While this sounds like technological motherhood and apple pie, it means that the Internet protocols are not the best choice for any particular purpose. They are, however, just good enough for most of them, and by sacrificing optimality the result has been a world of unplanned synergies.
A second is scalability. The Internet protocols don't contain performance numbers that impose assumptions about how they will be used, which has allowed their performance to be scaled over 6 orders of magnitude, far beyond anything initially anticipated. The only real exception to this was the address size, which is the one thing that's needed to be fixed.
Third is the end-to-end principle: the functions of the Internet are defined by what is connected to it, not by how it is constructed. New applications can be created without requiring anyone's approval, and can be implemented where information is created and consumed rather than centrally controlled.
And a fourth is open standards. The Internet's standards were a way to create playing fields, not score goals; from VHS vs Betamax to HD-DVD vs Blu-Ray, the only thing that's changed in standards wars has been who's sitting on which side of the table.
These simple-sounding ideas matter more than ever, because the Internet is now needed more than ever, but in places its never been. 3/4 of electricity is used by building infrastructure, which waste about a third of that, yet many of the attempts to make it intelligent hark back to the world of central office switches and dumb telephones. Some of the poorest people on the planet are "served" by some of the greediest telcos, while it's now possible to build communications infrastructure from the bottom up rather than the top down. In these and many more areas, four decades of Internet development are colliding with practices brought to us by (presumably) well-meaning but ill-informed engineers who don't study history as part of an engineering education, and thereby doom everyone else to repeat it. I'd argue that we already know the most important lessons of the Internet; what matters now is not finding them, but making sure we don't need to keep re-finding them.