So let's say we've discovered a nice habitable planet around those nice, nearby sun-like and well-behaved stars, Alpha Centauri A or B. How are we going to get there? As it stands, there are three possible ways of getting there. Obviously it's going to take a long time.
The simplest in engineering terms is hibernation (aka "suspended animation"). This has the very important engineering advantage of not needing all the mass of a big habitat or a closed ecology. The ship can go faster or be smaller (and cheaper) as a result. Throw the humans in the hibernation chambers and let them sleep the journey away. Plus they won't go stir crazy or forget how to do their jobs. However, there are significant challenges: we don't really have the first clue as how to induce hibernation in humans.
Short-term hibernation is possible through induced (or accidental) hypothermia. Unfortunately it's dangerous - Swedish radiologist Anna Bågenholm was dunked under ice with a core body temp of 13.7°C. A drop below 28°C is often fatal. However - this hypothermia-induced hibernation can be extended for long periods. Mitsutaka Uchikoshi, a Japanese skiier, went missing and was recovered 24 days later with his organs shut down and his body temperature at 22°C. What was particularly amazing was how he survived for so long without any fluid intake.
Hypothermia can also be induced for medical reasons (with much better prospects of surival as it's controlled): English and Japanese doctors pioneered the technique of using deliberate hypothermia for heart surgery with packs of ice, and the Russians perfected the technique (the normal solution these days is to use a heart-lung machine). Basically the brain chilled to about 16°C (60°F) and the body to 24°C (75°F). This gives the doctors a 30 to 60 minute window where the heart stops and they can tinker with it, then whip the body back up to full temperature with no lasting brain damage. A recent discovery with mice showed that hydrogen sulfide combined with hypothermia could be used to induce hibernation in mice - but only mice. It probably won't be as simple with humans, but the US military is certainly interested in it for trauma applications. Extreme hypoxia might also be a trigger.
Unfortunately, humans just aren't built for hibernation; this technique must be done correctly otherwise there is severe risk of cardiac arrest. More so is the problem of simply lying inert for years on end. Wouldn't the body degenerate? What crucial processes might be impaired? It might be necessary to wake the sleepers up every year or so to let them recover, before climbing back in the freezer again - with significant impacts on life support requirements.
For really long term flights, it might be necessary to go all the way and use cryogenic preservation - ie freezing the astronaut solid and then thawing him/her out. Unfortunately, this is kind of problematic - small embryos and organs can be successfully quick-frozen, but damage from expanding ice crystals (especially during re-warming) causes all kinds of havoc. A way around this is vitrification - basically pumping the body with antifreeze, turning the body into a block of glass at -135°C. This unfortunately creates further problems in the form of the toxic antifreeze now flushing the body.
The most likely scenario - hibernation through some combination of induced hypothermia, hypoxia and drugs, seems feasible enough that we could conceive of an interstellar mission if the propulsion technology is likewise developed (which seems to be the far more difficult problem). Since hibernation has many more applications than just long-duration spaceflight, it'll probably be developed sooner rather than later.
The hibernation "pods" would probably be some small climate-controlled chambers with a comfy bed, IV drip and some sensors, hardly weighing anything at all. More like the cheap-looking hibernation pods in the original Planet of the Apes than big bulky cryo-coffins. They'd be located right in the heart of the ship, surrounded by as much radiation shielding as possible, and with a bit of rotation to keep fluids behaving properly. The quarters for the awake crew would probably be right next to it, to take advantage of the proximity to the sleep chambers' radiation shielding. Upon arrival, the sleep chambers could be used as bunks for the crew.
Reliability of the hibernation mechanisms would be a big issue - springs, one of the most reliable components, rarely last beyond 60 years. New, highly fatigue tolerant materials need to be designed, along with fault tolerant systems - more so than with a ship where everybody's awake and able to fix things. This in itself is a significant challenge, but the aerospace industry tries to reduce maintenance and extend aircraft life to lower operating costs, so this is another area where industry may make the development anyway.