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"How fast" equals "what acceleration" times "how long". There are a number of proposed designs for "nuclear space drives", from the Orion Nuclear Pulse Rocket to NERVA to ion engines.

The only "nuclear space drive" currently in use is a ion engine in use on an unmanned probe. The acceleration of the rocket is very very tiny - but it runs for months at a time, building up a respectable velocity.

The problem with conventional rockets is that they have very high accelerations - for about 6 minutes. Then they are usually out of fuel, or nearly so. Nuclear propulsion has the POTENTIAL - as yet only dimly realized - to allow the engine to continue to operate for long periods of time at much lower accelerations, but building up tremendous velocity because of the duration of the thrust.

So I guess the "real" answer to "how fast" would be "We don't know yet. But eventually, VERY fast."

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