The most common instruments people use to study volcanoes are called seismometers, which are the same things that you use to study earthquakes.
Seismometers are a pretty simple instrument that measure how the ground shakes or vibrates. For example shaking can move a pen across a roll of paper to record how intense the shaking was. Modern instruments are a bit more complicated but the idea is the same. By collecting a lot of this data you can put it into a computer program that can model what is going on inside the volcano (like how the lava/magma is moving around and where it is).
Geologists also will go to active volcanoes to sample lava or gases to get a better understand on what is going on inside the volcano.
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