The quickest way is indeed a water change.
Alternatives include chemical systems, like the nitrazorb mentioned, although there are a few others.
The other options are nutrient export, done in the display in a planted tank and often done with macroalgae or algae scrubbers in marine systems or biological methods with nitrate reactors (essentially anaerobic systems that run the nitrate process backwards up to gaseous nitrogen, which then gasses off).