The world's first engineering study of an unmanned spaceship to explore one of the nearer stars was made by a technical group of the British Interplanetary Society between 1973-77. The target selected for the exercise was Barnard's Star, nearly 6 light years distant from Earth. The contributors recognised that the work, based on the technology extrapolated to the beginning of the 21st Century, could represent only a first approximation to the solution of starflight.
The results showed it would be a formidable task requiring a massive craft that would dwarf the Saturn V moon rocket, the largest space vehicle yet flown by man. Daedalus, as currently conceived, would weigh some 54,000 tonnes, nearly 20 times the weight of the Saturn V, carrying nearly 500 tonnes of fully automated payload. Because of the enormous time lag involved in radio communications between the Earth and the ship, a semi-intelligent computer would have to control the entire ship and work out all actions necessary for the exploration phase of the mission.
The result was a two stage, nuclear fusion powered vehicle, unmanned and under autonomous operation due to the distances involved, accelerated to 16% of the speed of light, and armed with a variety of probes, sensors, robotic wardens and intelligent decision making computers. Although the journey could take as long as 40 years, a flyby at such speeds would be over in 70 hours.
Although the study was conducted during the 70's, it's still referred to today, even in NASA, as a baseline study. Any future mission to the stars probably won't look anything like Daedalus, but it gives a good idea of the complexity and scale of task, and the length of time it would take to get to even the closest stars.
No estimate of the cost of such an enterprise could be made, but it would be way beyond the capacity of an individual nation, and would probably need a period of world stability unlike any we have seen to date.