Thanks to the efforts of Elon Musk and those working with him, it is likely that we will soon become a multi-planetary species. In this post I consider what we need to become a Multi-Galactic species within our lifetime. First, I want to establish a few ground rules to eliminate some obvious methods to cheat our way to this goal.
1 : No Immortality
While longevity technology will certainly advance quite significantly in the next 50 years, this isn't what I mean by "in our lifetime".
2 : No faster than light travel (It's the law!)
While we may stumble across warp drives or wormholes in the coming years, we can't count on it, so we should plan accordingly. This includes faster than light communication.
3 : No magical energy sources
Zero Point Energy, and similar concepts of pulling energy out of the universe are neat for sci-fi, but unnecessary to achieve these goals.
I believe it is possible that the first humans to set foot in the Andromeda galaxy could very well already be alive today.
In general, the trick here is to get a spacecraft constantly accelerating at 9.8m/s^2. Not only will this rate of acceleration be maximally comfortable to the passengers, since it would perfectly simulate the gravity of earth, but the craft would very quickly reach relativistic speeds. To passengers on this ship, a journey to Alpha Centauri (4.37 light years away) would take ~3.6 years (while 6 years would pass on earth). It would take about 14 years to get to our new earth-like neighbor, Kepler 452-b (1400 light years away). Finally, Andromeda, at a distance of 2.5 million light years, would take about 28 years of travel from the perspective of the passengers on board. By the way, the travel time is nearly cut in half if the passengers are willing to get pushed at 2g.
You may notice from those travel calculators the insane amount of fuel required to make such a journey, but what if the ships didn't need to carry any fuel at all? I think the most realistic way forward for interstellar, and ultimately intergalactic, travel is for our stars themselves to constantly beam the required energy directly to the vessels in flight.
We have already shown that we can very efficiently convert energy fired from lasers back into useful power using "reverse lasers". Energy sent this way could be collected, directed, or reflected, and used by something like a solar sail, or maybe to charge a photon rocket. This is along the lines of existing laser propulsion systems, such as the one that promises to send crafts to Mars in 3 days.
Of course, there are many scary pitfalls of traveling like this. Losing contact with your power source could potentially leave you stranded, which is why it is also important to build a network of these systems on any star we can reach. I imagine our system here at home would be a network of satellites orbiting our sun, like a Dyson Swarm that collects energy from the sun and very carefully fires it towards customers. Presumably, before any humans are sent to other star systems, a kit of equipment would be sent ahead first, and since no humans will be aboard, they could potentially arrive much sooner, and have time to establish the communication requirements to "catch" incoming ships. If there happen to be sufficient resources around the star, the satellites could even establish mining operations, and build more satellites to send out to nearby neighbors. This network of colonized stars could also act as a galactic communications grid.
Interestingly, because of how drastic the relativistic effects of intergalactic travel are, by the time we get to Andromeda, every star could be completely mapped, categorized, terraformed, and ready for its new human inhabitants.