Based on what we *know* right now, our best-bet is to build a series of self-sustainable "generation ships"; (very-large spacecraft, capable of sustaining human life over the course of several generations, including the necessary ecosystems to support such life.)
Such technology is at least theoretically do-able, from a technical standpoint.
From an ECONOMIC standpoint, of course, it is as impossible as faster-than-light travel. To expend the money required for such an enterprise, to send-off one or more such "generation ships", with no possible ROI within the lifetime (or thousands of lifetimes) of the investor, is not something that can be done with a civilization that does not even want to invest the money to educate their own children.
And this would only happen if we knew, for certain, that the destination worlds were inhabitable. (and not yet inhabited). And even if they were, we would have to wait thousands of years for the colony to develop to the point of economic viability so that they could even send a response.