Colonization in our solar system is just a matterwaste of time.
Beyond that...other solar systems, I only wish to speculate so far. Our abilities will be vastly different when we are ready to try such a task.
Re: colonization. For what purpose? The technology to control Earth's population has been around for decades. It's called condoms and birth control. As other nations industrialize, their birth rates should drop. There's no reason why governmental policies and a slow cultural change couldn't effectively result in a very sustainable population on Earth - say, 5 billion. Or even 2 or 3 billion; that could happen in a matter of a few generations, if there was the will. We don't HAVE to outgrow our planet and resources.
Thus, as far as needing room for Earth's population, such a need would be artificial. Further, colonization would NOT be for this purpose. The energy required to get significant numbers of the population off our planet is mind-boggling, though something like space elevators would reduce the required energy to about the minimum possible. I'm reminded of a talk about physics and comics at the American Association of Physics Teachers - a fairly common theme is that the evil-doer or good-doer is soooooo close to an invention, they're just missing one final ingredient. And, that's all that's missing from space elevators being a possibility - one final ingredient. But, no one knows what precisely that ingredient is going to be. Calling it "unobtainium" isn't necessarily incorrect. *IF* the ability to build space elevators ever comes to fruition, I'll be celebrating that event with the type of enthusiasm as someone celebrating their marriage or birth of a first child.
Now, about these other solar systems. At this point, it's absolutely magic. Maybe, one day, something will be discovered that will get us there. At present time, we absolutely do NOT have the technology to get there. Look at the calculation earlier in the thread - to send the International Space Station to a solar system 10 light years away, in a journey that took 200 years, it would take the equivalent of ALL the energy used by humans in the course of one year - all of the coal, all of the oil, all of the natural gas, hydropower, solar power, wind power, and nuclear power put together.
It was easy to overlook this point: the calculation is based on the present weight (mass) of the ISS. The amount of energy required scales up nearly linearly with the mass of whatever we send people on to another solar system - and since you have to take fuel with you, the equivalent amount of fuel used on Earth in a year - your mass is going to increase tremendously. Let's not forget all those supplies the ISS gets from time to time; 200 years worth of supplies have to be taken on the journey. To send 20 people to another solar system, I think it would be an extremely low estimate to say, 20 years worth of all the energy used on Earth.
Though, if we ever master fusion power (ahem, dear Gov't, please fund this research), it may be possible to gather up those half dozen or so hydrogen atoms per cubic meter - I have not done the math though on this possibility. Other ideas, such as warping space, are still well within the realm of science fiction. Just because we can imagine it does not mean it's ever going to be physically possible. (I would LOVE to be wrong on this one.) But, it's sort of like Micchio Kaku constantly talking about invisibility cloaks, etc. What I don't think he has ever mentioned, when talking about how in the future, it blah blah blah, that the technique they've come up with for building them has a very solid drawn in the sand line that has to do with the particle sizes that are arranged in the meta-materials. Simply, the physics does not allow for building invisibility cloaks that cloak visible light, because the particle size would have to be too small (smaller than atoms). Or, to put it another way, "look! Jimmy built a 1 foot tall building out of silly putty. One day, mankind will be able to build 1000 meter tall sky scrapers out of silly putty." Hopefully, you realize such isn't possible because the inherent properties of silly putty would cause such a building to collapse under its own weight long before it came even close to that height. Structural engineering (with the constraint that silly putty be used) is never going to overcome the physical properties of that squishy substance. So, even though we can teleport sub atomic particles, and possibly are on the verge of warping tiny tiny tiny amounts of space, it does not automatically mean it's just a matter of time before we're flying an Enterprise at warp 2.