In order to send a spacecraft to another star in an amount of time that would strike the average person as reasonable — like a generation — we're going to need new ways of propelling the aforementioned spacecraft that would strike the average person as nuts, like using solar-powered lasers to coax antimatter fuel out of the quantum vacuum of space.
This whole idea of creating something tangible (like fuel) out of a total vacuum seems a bit far-fetched, but it's been done before in a lab. Last year, we wrote about an experiment that used a highly energetic vibrating mirror to turn "virtual" microwave photons into real ones, essentially creating particles from nowhere. This works because on the quantum level (at very very small scales), a vacuum isn't really a vacuum, but is actually a sea of "virtual" particles that are constantly going back and forth from existing to not existing. With enough energy, it's possible to yank those particles into existence permanently and do stuff with them, and this is the concept behind the VARIES starship.
VARIES stands for "Vacuum to Antimatter-Rocket Interstellar Explorer System." It's a fairly conventional antimatter-fueled rocket system, but the unique part is where it gets the antimatter from in the first place. VARIES is equipped with a gigantic set of solar panels, each of which is hundreds of square miles in area. To fuel up, VARIES parks itself next to a star, and then uses those panels to power a truly monstrous laser that has enough power to smash the vacuum of space itself, spontaneously generating both matter and antimatter (protons and antiprotons) until it's got enough reaction mass to make it to its destination. As long as VARIES can find enough solar power, it can create a virtually unlimited amount of the most efficient fuel that we know of.
While the principle here is (apparently) sound, we're not very close (yet) to being able to produce a laser powerful enough to generate the electromagnetic field required to create matter and antimatter out of a vacuum. The critical point is about 5 x 10^29 watts per square centimeter, which, while a heck of a lot more than this, is not totally out of the realm of possibility in the intermediate future.