There are several things to think about: the design of the ship, the size it would need to be, power generation, how to provide gravity, how to produce food and water, and propulsion.
It seems to me that one, if not the, major problem to solve for this type of voyage on this type of ship will be propulsion. There has been much thought given to this problem already (see articles on the Bussard Ramjet, NASA propulsion systems of the future, Ronald Litchford’s paper on Strategic Technologies for Deep Space Transport, and the Wikipedia article on Interstellar Travel). It stands to reason, I think, that this type of thought and research will continue. I’m simply going to assume that the problem will eventually be solved, and I won’t worry about the details here.
There has also been a bit of speculation about ship design… – partitions, power, propulsion, gravity.
Environment on the ship – storage for everything for the trip, or an ecosystem to produce food and recycle waste?
How fast and how long? Time dilation and compression.