Steven Hansel said:
Let's say we already colonized some of the planets and moons in our solar system. Mars,Moon, Europa and etc. Planets like Mars and other has less gravity than earth, so the resource needed for space travel in our solar system will reduce by a lot if we launch spaceships there. Say, that we already can do asteroid minings by 2030. How long will it take for humans to colonize planets in other solar system?
I guesstimate that we'd need a few centuries from today to send the first interstellar manned ship.
First, Solar system colonization.
It will require huge advances in such areas of technology as: closed life-support systems, space habitats, space-based industry, space-based food production. Right now, we are at best rudimentary in those.
Substantial progress will be needed in medicine (humans living in low- and zero-G, higher-radiation environment), power sources (say, fusion reactors?), engines (ion, fusion?).
Of course, all the other sciences would not stand still either, so expect computers to become faster, better (lighter/stronger/...) materials developed, etc. Observational astronomy will have much better data on the nearest stars and their planets. Perhaps even images of continents on them!
Solar system colonization can also result in many more people living (say, 200 billion humans by 2200?), thus having bigger economy.
With such scientific/industrial base, I imagine building of a ~0.1c ship would be possible. That is enough to reach nearest stars.