Xinxiang has no local airport. The nearest airport is Zhengzhou's Xinzheng Airport.
Most trains that stop at the capital city Zhengzhou will also stop in Xinxiang. You can take either the normal train (which takes about an hour) or the high speed train (which takes less than 30 minutes).
Be warned that if you are taking the normal trains, they are usually quite dirty, with their windows closed, and packed to the brim.
You can take a bus from Zhengzhou to Xinxiang, it takes roughly 1.5-2 hours. The bus station is next to the train station.
There are also many 'illegal' taxis or car-sharing services that transport people between Xinxiang and Zhengzhou.