Hi Michamus,
I don't know much on the topic myself, and I expect cavediver will be around to explain it much better for you. But here's how I understand it:
Velocity is always relative. That is, for instance, there's no such thing as traveling at an absolute speed of 0.999c. It is always relative to some other object.
So while light will always be leaving you at the speed of light, the relative velocity, or change in position over time, will always be sub-light speed for any given reference frame.
However, because of length contraction, if you were able to approach some coordinate, say a distant star, at a speed close to the speed of light, the distance would appear much shorter, and you'd be able to get there quickly. From an observer on earth it is not the distance that is getting shorter, but your spaceship. The observer would see time dilate on your ship, but would experience it as if your ship took many years.
So if you really wanted to get to a distant object within your lifetime, you would never have to exceed the speed of light. Just don't expect your friends to still be waiting for you when you get back.
Respectfully,
-Meldinoor