There are various methods of stream gauging or installing control structures like flumes or weirs with control dimensions, where water levels can be recorded.  Otherwise, a stage discharge relationship must be developed for stable cross section.  Transducers like from Global Water or Onset Hobo (examples) are relatively inexpensive, can record stream or water stage at about any desired time increment but can sometimes clog if sediment loads are high.  Various floats or manometers have also been used.  For most complete information, the US Geological Service probably has the most with some searching at www.usgs.gov or searching on stream gauging methods.

Dear Roger,

A variety of hydraulic structures / primary device are used to improve the reliability of using water level as a surrogate for flow (improving the accuracy of the rating table), including: Weirs, V-notch, broad-crested, sharp-crested and combination weirs, Flumes, Parshall flume. Other equipment commonly used at permanent stream gauge include: Cableways - for suspending a hydrographer and current meter over a river to make high flow measurement, Stilling well - to provide a calm water level that can be measured by a sensor. Water level gauges: Staff (head) gauges - for a visual indication of water depth, Water pressure measuring device (Bubbler) - to measure water level via pressure (typically done directly in-stream without a stilling well), Stage encoder - a potentiometer with a wheel and pulley system connected to a float in a stilling well to provide an electronic reading of the water level, Simple ultrasonic devices - to measure water level in a stilling well or directly in a canal, Electromagnetic gauges.

You will find more details in these links.

https://fr.slideshare.net/BilalN22/stream-gauging-57269584

http://www.nws.noaa.gov/os/water/RFC_support/resources/WMO%20Manual%20on%20Stream%20Gauging%20-%20Field%20Work%20%201044_Vol_I_en.pdf

With my best regards

Prof. Bachir ACHOUR

Automatic gauge recorder may be installed at some stable section and from previous stage discharge record discharge rating relationship may be developed to convert observed stage into discharge.