The answer to this complex topic is the heart of the science of volcanology and its ultimate challenge.

While there is no easy and short answer, this is the essence: you combine knowledge of the volcano's specific past behaviour with all available observation of its present state, and this allows you to make a long-term and a short term prediction:

1) You study the volcano's eruptive behaviour in the past and ideally, you also try to find out wether there were any signs of change before its eruptions. Such changes might be: unusual seismic activity (i.e. earthquakes at the volcano), visible or otherwise detectable deformation of the ground (i.e. opening of cracks, swelling of the whole mountain etc.), changes in composition and temperature of fumarolic gases and so on.

2) Then you monitor the volcano's behaviour in the present, looking for such changes.

Based on the knowledge of the volcano's past, you can make a long-term prediction (example: sooner or later, Mount Rainier is going to erupt again, although nobody knows exactly when, but chances are almost certain high that this might happen within the next few centuries). The short-term prediction is possible when there are signs of change, and the more is known about the volcano and the more data are available about its present state, the more precise such predictions.