I'm copying this information from the Common Water Contaminants page, but would love to learn more ways to measure nitrogen as well; please help us compile different techniques!
The wet lab Kjeldahl Method is often used to get the measurement TKN, or Total Kjeldahl Nitrogen.
EPA Method 353.2 involves a cobalt catalyst and spectroscopy in the visible range.
TSS, BOD, and Nitrate with a single 200nm-720nm spectrometer ON-LINE NITRATE MONITORING IN SEWERS USING UV/VIS SPECTROSCOPY F. Hofstaedter, T. Ertl, G. Langergraber, W. Lettl, A. Weingartne
Potentiometric Measurements of Nitrate and Ammonium using Ion Selective Electrodes
Ion selective electrodes (discussed here) can be used to conveniently measure ammonium and nitrate. These electrodes behave similarly to commonly used pH electrodes. The main difference between a pH electrode and an ion selective electrode (ISE) is that the former has a glass surface that is electrically polarized by protons and the latter has a membrane that is responsive to the ion in question. Like a pH electrode, an ion selective electrode responds to changes in analyte concentration by a measurable change in voltage. Ion selective electrodes can be measured with most pH meters. These electrodes can be purchased from a variety of sources (VWR, Fisher, etc) but are somewhat more expensive than pH electrodes. Vernier sells ammonium and nitrate sensitive electrodes (here) for $179 each.