Musk said something about wanting to establish a Moon base.
First step is for the general public to be properly educated about history.
Second, inspiration is needed. Perhaps a bold, successful mission to at least orbit the Moon, which is being planned already. Maybe live-stream a broadcast from Lunar orbit(2-second delay and all). That would help inspire new engineers as well as public support for an adequate budget. An intelligent way of building public support would be to leverage people's other concerns into support for space. If they're concerned about global warming or overpopulation, sell them on expanding into space as the ultimate solution. This is what Musk is doing. Biomedical research could be done on the Moon that would be too dangerous to be done here. Cures for many diseases could be found. You could also sell the idea of Moon development as essential for security to the more hawkish, so no matter what you're views or concerns, space is an essential investment. "Sell" it.
Third, corporate interest(and sponsorship) could be generated by offering limited mining claims to be allowed. You pay for the rocket, you claim the rewards. Meanwhile, spacefaring technology benefits as a whole. A rising tide floats all boats.