Instruments that use the acoustic Doppler principle transmit a short pulse of sound of constant frequency into the water, "listen" to its echo, and measure the variation in frequency of the echo with respect to the initial pulse. In this case, and according to the Doppler effect, this difference in frequency is proportional to the velocity of the water. Actually, the emitted pulse reflects from suspended particles, typically sediment, plankton, or air bubbles, not from the water itself. If it is assumed that the scattering material is floating passively and therefore is moving with the same speed as the water, the velocity of the particles (measured) may be considered as the velocity of the water surrounding them (inferred).
ADCP stands for Acoustic Doppler Current Profiler. An ADCP uses aforementioned Doppler principle to measure the water velocity at different distances from the source of the acoustic signal. If the instrument is sitting on the bottom of a body of water, i.e. it is moored looking upward, it will measure the water velocity at different depths. In other words, a moored upward-looking produce a profile of water velocities from its current measurements. Sometimes they include a pressure sensor that provide a way of measuring water level variations.
There are different types of ADCPs that depend on the frequency of the instrument (typically in MHz), the sampling interval (or frequency, in Hz), and the sampling scheme (continuous or in bursts). According to these, you may be able to measure in different environments (nearshore, inner-, mid-, outer-shelf, open ocean, rivers, fjords, estuaries) and different kinds of processes (surface gravity waves, river discharge, tides, sub-tidal currents).
From the numerous options in the market, I selected the two companies I have worked with and included them as follows. The aim of next few lines is to give a glimpse of two companies that manufacture ADCPs. I am not trying to advertise their products, although they are of high quality :)