In a sentence: by increasing the amount and quality of physical goods (through automation) via freely available open-source channels, until it makes no sense for anyone to rely on anything else.
The transition beyond our current institutions to post-scarcity, due to social and political reasons, may though be harder than actually developing the technologies required to support a technological post-scarcity.
However some form of true post-scarcity - perhaps regulated at the personal consumption level unless agreed at a community/regional level for larger projects - where all people on Earth do not have to work for pay, or any kind of exchange, and have a very high standard of living does appear possible on the face of it. The Earth's crust contains quintillions of tonnes of useful elements; energy is plentiful (solar, geothermal, nuclear) and automation of everything significant including the fabrication of other automated systems is likely to be within mankind's capabilities. Open-source design and engineering would be the development model.
Potential routes to transition to post-scarcity
Here are three methods of how, it might be possible to transition from our current economy to a post-scarcity (there may be others of course):
1) Advanced digital fabrication and closed-loop operations on a local scale - think of a very advanced version of Open Source Ecology who are operating at a small farm-scale.
2) Let industry compete to zero-cost (or infinitesimally small cost) through automation. The companies could be helped along by employing some open-source systems in their operations (and even contributing to OS projects) to reduce their costs in non-core areas. With companies in all industries eventually doing this to help them compete, the non-core areas from each industry may eventually all overlap, joining together to provide a complete alternative open-source infrastructure.
3) Intentional duplication of all key infrastructure, manufacturing and services to eventually create a parallel automated open-source economy by open-source advocates - much as was done in the software world, developing C compilers, operating system kernels, graphical desktops, IDEs and key applications. It took a while to get that all in place but eventually it got to a stage where Linux could be a primary OS for developers and geeks (about 10 years), and now it is perfectly usable for normal computer users (after about 20 years).
Power, control and jobs
A common argument is that existing people / companies / systems wouldn't let it happen - however it is simply another form of competition. In the same way, having established companies around doesn't stop startup companies from forming and operating either. Incumbents can certainly make things difficult, but they are unlikely to be able to stop it happening altogether. If it is open-source and free (or lower cost than a commercial alternative) then the commercial producers and distributors may have a hard time competing if the goods or services from the open-source producers are of a similar (or even slightly lower) quality. You could argue that open-source networks and organisations operating at cost (and driving it towards zero) during the transition period are perhaps the ultimate example of effective market economics at work.
As an example, Microsoft couldn't stop Linux being developed and used globally often in direct competition with their consumer and business software (although they tried hard). There is estimated to be around 33 million computers  running a Linux-based operating system (including the Android mobile phone OS), and those are just the machines that are browsing the web. This figure probably doesn't include the millions of server computers which run Linux, and is in fact the dominant OS in that sector with about 60% of machines running some flavour of it.
Open-source hardware is still very nascent, but an interesting example in the physical (rather than software) world is the open-source RepRap machine, where it and its derivatives now make up a majority share of new FDM 3D printers, according to Dr. Adrian Bowyer, an academic at the University of Bath and founder of the project.
Human progress since the enlightenment has been rapid and continually disruptive to the apparent status-quo. This is still very much the case today, and near-future mass-scale open-source products and services are a continuation of this. The buggy-whip manufacturers will always complain about disruptive change of course, but consumers will be getting greater choice for less and less cost. How jobs will be affected though with advancing automation is another issue altogether.
Interestingly as the average person's earning potential perhaps goes down as automation increases, the more easily and cheaply people will be able to get goods and services from automated open-source systems, so it may balance to a certain degree. One extrapolated end-point is that as people's earning potential gradually falls to zero over time, all significant product and service costs will also be tending towards zero. Another (rather pessimistic) alternative scenario, is that as automation increases, fewer and fewer people are able to afford the products produced by the dominant companies. This seems unlikely as commercial entities wouldn't be able to survive if there were too few customers in that market, so they might as well end up giving things away by the time all significant production is done 100% by machine, because what does it matter if all the companies costs were followinng the same path too? However if the companies didn't do that, it wouldn't matter anyway as the open-source providers would take their place. This seems to be inevitable barring some kind of governmental intervention. None of this would happen overnight so society would have adjust, as it always has done. This is why we don't still live in the stone age.
At a personal level
Imagine a world where you can grow all your own food in a fully automated greenhouse. Your water falls freely from the sky or wells up from the earth and is filtered and cleaned automatically. Any time you want a new device or product, you can find a design online, perhaps customise it, and fabricate it locally or have it delivered using an efficient automated delivery service. And your children have access to the best education ever conceived, for free and you have access to abundant free energy. What need will you have then to you engage with the monetary economy?
The way to bring about a global post-scarcity economy is to help add to the commonly-held resources of mankind. Learn how to grow your own food and give the seeds and the exact method of growing away for free on the Internet. Contribute to open-source educational materials. Study whatever you're passionate about and think how you can use it to add value.
Social change doesn't come by decree from the politicians' halls. It always comes from the bottom up, from the young vibrant minds who see clearly and say, "I can see a better way to do things". Many grass-roots and open-source type projects are making a real difference in the world right now, so join an existing one or you could inspire others and start your own.
The universal commons is the store of information freely available to mankind. It is all about information, and information-management is now the key determinant of success in food production and medical care — and digital fabrication will make information the only non-trivial ingredient in physical goods. This trend towards information-rich activities is important because sharing information is non zero-sum, meaning that I can give it to you without diminishing my own supply. If information determines the production of other resources, and that information is free along with abundant material and energy, then global abundance should be possible. Advanced digital fabrication and universal access to information are expected to improve by several orders of magnitude over the course of the next few decades...