Methods to measure gas and water vary depending upon the level of volcanic activity

Gas concentrations (relative amount of a specific gas) and emission rates (how quickly the gas is released) are measured using airborne or ground-based techniques both in times of relative quiescence and during elevated volcanic activity. Large gas plumes can even be measured by instruments mounted on satellites orbiting the earth.
Ground-based direct measurements can be made during non-eruptive times
One method for sampling volcanic gases is to collect them directly from fumaroles in evacuated flasks or solution-filled bottles, and then to analyze the mixtures in the laboratory. This type of "direct sampling" of gases escaping from fumaroles is currently the only way to (1) fully characterize the composition of gases discharging from volcanoes; and (2) collect isotope data needed to determine the origin of specific gases.
Direct sampling via soil-efflux surveys can be made in areas where carbon dioxide rises from depth and diffusely discharges into the atmosphere. Dozens of measurements are typically needed to map areas of high gas concentration. One site where soil-efflux measurements have recently been made is near Horseshoe Lake at the base of Mammoth Mountain volcano in California. Here, a large area of trees has been killed by carbon dioxide emissions near the northern shore of the lake.
MultiGAS instruments can also be used for direct sampling and efficiently monitor several gases at once. Using a combination of optical and electrochemical sensors, these instrument packages can measure the concentrations of CO2, SO2 and H2S as well as environmental parameters like temperature and pressure. They are typically carried to fumaroles or degassing vents during measurement campaigns or even installed permanently at locations downwind of such vents. Instead of collecting gases for later analysis, the collected data can be transmitted by radio to a volcano observatory providing a minute-by-minute record of changes in gas concentration.
Discharge rates of some gases can be measured from a distance
Direct gas sampling can measure the relative amount of gases (concentration), but it does not provide information about the emission rates–this is where remote sensing techniques excel. A COSPEC or DOAS spectrometer measures the amount of sulfur dioxide in a plume cross-section by transecting beneath a plume or scanning across it. Multiplication with the wind speed gives the SO2 emission rate – the amount of SO22 emitted into the atmosphere every second, hour or day. DOAS instruments attached to satellites can be used to detect very large SO2 plumes.
Due to the natural background concentration of carbon dioxide in the atmosphere, remote-sensing techniques cannot easily detect volcanic CO2.