Space is mostly empty and much of what you see while in it is very far away. So there isn't much you really do visually; fundamentally you're mostly going to be working with variants of "white lines around the subject" (speed lines, possibly elongated as the ship's speed increases, the occasional bit of "space debris" or dust particles zooming by) and FOV changes. In addition, you can play with subtle camera shake or distortion effects as the ship's speed increases. If it is thematically appropriate you can use a "hyperspace" like tunnel or wormhole (or really, anything) effect when you're traveling at super-light speeds, maybe. But that's basically it; there are very few other objects that both provide a visual frame-of-reference and are also regularly close enough to a ship in most space games to really illustrate the magnitude of the ship's velocity.
However, you can also work with non-visual cues. Specifically audio, physical and gameplay cues.
Audio effects such as engine whine or rumble can give a sensation of a powerful engine being put into gear, especially when paired with screen effects like a camera shake or FOV animation. Fly-by sounds for those rare cases where the ship does pass near something moving at a significantly slower relative speed.
Physical effects (mainly, force-feedback) can be fed back to the player during acceleration or when nearing "top" speed, if the player has the appropriate hardware.
Gameplay-wise you can alter the maneuverability or responsiveness of the ship based on its speed. Maybe it reacts more slowly to attitude adjustments at higher speeds, for example, or "fights" the player via force-feedback or slightly less smooth controls.
Most of the above are wholly unrealistic, so depending on the level of realism you're going for in your simulation you may not be comfortable with including some of them.