Plants use nitrates as a fertilizer so planting up the tank a bit more will help reduce the nitrate levels, but make sure you have the right strength lighting for your plants so they grow well because if the plants start to die off they may actually make the nitrate problems worse. Adding more filtration to the tank can also help reduce nitrates as well as doing small to medium sized water changes as previously suggested etc.
Most terrestrial plants use nitrates as fertilizers. Most aquatic plants actually prefer ammonia as their nitrogen source. In fact, most aquatic plants will take up the nitrate, then convert it to ammonia (doing the reverse of the cycling bacteria) and then use it. The plants will take up the nitrate, but only lastly -- as andy said, they will prefer to take up the ammonia first. Now, if there is no ammonia for the cycling bacteria, that means no nitrates will be made at end of the cycle. In the end, the plants do help take up the nitrates, but I just wanted to note that it isn't quite as straightforward as Tokis said there.
