The closest star to us is called 'Proxima Centuri', and from the name 'Proxima', you could be forgiven for thinking it must be quite close. In galactic terms, it is. In real terms, with our current capabilities, it really isn't.
Proxima Centuri is 4.5 light years away, meaning quite literally that light takes four and a half years to get there. And we can't yet travel at the speed of light. Using the technology we currently have, and applying a lot of goodwill to it, our best option would appear to be nuclear electric propulsion, which is at the testing stage with several space agencies, and has the potential to be put to great use in interplanetary travel; it could reach Mars in as little as 90 days. To reach Proxima Centuri, however, would still take a little in excess of 1,000 years. We hope there isn't a galactic neighborhood notice board pinned up in one of the nearby star systems - at the moment we have very little chance of being able to read it.