The time dilation effect is pretty well known and comes naturally from the equations of the General Relativity Theory.
It's also been proven experimentally in particle accelerators (like CERN) when particles with at rest very short and well known half-lives (i.e. they natural break down into other particles some time after being created) lasted a lot longer (from our point of view) when travelling at near light speed.
However that effect only really starts getting noticeable without special equipment when the speed something is travelling at is getting near the speed of light (something like 90% or more of light speed).
This works correctly for the example of the previous poster because the distance to Sirius is given in light-years, which is literally the number of years that takes light (which by definition travels at the speed of light) to travel that distance.
(By the way, from the same equations from were you get time dilation comes that from the point of view light the trip is instantaneous)
So yeah, travelling a distance of that takes light 9 years to travel would be theoretically possible to do so fast (near light speed) that it would seem for those doing the trip to only take a few months (even though for those outside it would still seem to take longer than 9 years - as it takes light 9 years to get there so something at sublight speeds would take longer than the 9 years that takes for light).
Yeah, this is highly counter intutive so it "feels" wrong. If fact, the whole General Theory Of Relativity is highly counter intuitive. Yet, quite independently of what intuition (which is just a destilation of our personal experience) tells us, all that we've been able to observe so far in applicable situations is things happenning as predicted by that theory, not "intuition".
