Interstellar travel may as well be magic at this point in our development. Ignoring that, one way to get 1 gravity (G) in a spacecraft is to accelerate continuously at 1 G until the midpoint in the trip, then turn the ship around and decelerate at 1 G for the rest of the way. During such a long trip, speeds would get relativistic. Light speed (C) cannot be exceeded, so acceleration would constantly decrease by applying constant thrust to an increasing mass. (Mass increases greatly as it approaches C.) But the passengers would feel like they are accelerating at 1 G, and in fact, there is no way for them to determine that they aren't. As far as they can determine, they will be reaching speeds in excess of C. This happens because time distorts as well, according to relativity. Their time will slow down.
Real time to get there will be, oh, maybe centuries. (I lack the specific knowledge to calculate this time, though I'm sure it's doable. Plug the distance, acceleration, and deceleration into the right equations, and out pops the result.) But the passengers won't age nearly that much.