Space.com covers several ways to potentially get to our nearest instellar neighbor, Alpha Centauri. Interest in sending a probe or a long term mission to the star has been increased by stellar modeling that indicates a high probability of both planetary formation and a strong possibility of a terrestrial type planet in the star's habitable zone. The distance and time required, of course, are both a substantial challenge.
"Sending a person to Alpha Centauri within a human lifetime wouldn't be easy. Alpha Centauri is 4.37 light-years away — more than 25.6 trillion miles, or more than 276,000 times the distance from the Earth to the sun."
A conventional rocket would be impossible to use, taking far to long - a shuttle rocket would require 165,000 years. This has mostly to do with the fact the shuttle uses up is fuel at a prodigious rate. What is required is a method of propulsion that would either sip fuel slowly or gather it along the route, slowly gaining speed (like rolling a stone downhill) at an ever increasing rate, a "constant boost" method. One possibility might be Star Trek like anitmatter engine, although warp drive is probably a long ways off. Unfortunately, only small amounts of antimatter can currently be created at one time and it requires a huge particle accelerator to do it. Storing it safely for even a short time also requires huge magnets - defeating the purpose of a powerful lightweight fuel with a enormous mass for storage.
Another method I alluded to earlier is to gather your fuel as you move along the route, like a ramjet does in the atmosphere, as proposed by astrphysicist Robert Bussard many years ago. Unfortunately, the interstellar medium is nowhere near as dense with the required type of deuterium hydrogen atoms as theorized by the good doctor. A third method could be the "solar sail" method, which utilizes the interstellar solar "wind" created by the Sun's photons. Again there is a problem - the "wind" dies down the further you get away, and you would face a headwind when you started to approach your destination. One way around this would be to use orbital or Lunar based lasers to generate a light "wave" for the spacecraft to ride. However you would need an extraordinarily powerful laser, and laser tend to disperse over distance. Neutrally charged particle beams might provide an answer to this, so it might be the most feasible idea in the short term.
The most radical idea would be nuclear propulsion, where the vehicle is propelled by the repeated explosion of nuclear weapons, with the spacecraft protected behind a "shield". And you thought the environmentalists were aleady in a tizzy. Such a "pulsed proplusion" system works most efficiently on very large craft, however, so sending a colony of a 1000 people would be more feasible than a 1 ton probe. Jordin Kare, a Seattle-based technical consultant on advanced space systems, has come up with a blended "sail beam" system, using laser pulses like bullets to propel many small sails.
One option not mentioned is ion propulsion, but perhaps this is because it is already been deployed, for instance on the dwarf planet/asteroid mission to Ceres and Vesta which orbit between Mars and Jupiter. Such engines create a very small amount of thrust, but use fuel rather sparingly and thus could achieve a fairly significant speed, particularly if coupled with the standard "gravity assist" method to achieve relatively high rates of speed and "sling-shotting" probes all over the soalr systems, such as the Pluto probe New Horizons, or the Voyager missions.