Assuming the recently announced deep space travel project [1] works out and their estimates are correct (unlikely), it would take 20 years of preparation + 20 years of travel + 4 years of data transfer.

Also mentioned in [1] is that if Voyager 1 was headed for Alpha Centauri it would take 70,000 years.

[1] http://www.nytimes.com/2016/04/13/science/alpha-centauri-bre...