Well, there are lots of ways to know if a volcano is erupting. The most obvious way is if you can see ash or lava coming out of it. In that case scientists usually rely on seismometers.
Volcanic eruptions generate a lot of earthquakes.
These are almost always pretty small earthquakes that you can only feel if you are right on the volcano. If you record harmonic tremor on your seismograph then you can be almost certain that an eruption is going on somewhere.