What might a scientist look for to collect evidence about the formation of a volcano?

One thing to consider when answering this question is whether or not you are thinking about the formation of an ancient/existing volcano or the future formation of a volcano. While the difference is not too great, there will be some pieces of evidence that will change.
One thing that a scientist would look for is tectonic plate activity. Most volcanoes form along plate boundaries. Shield and fissure volcanoes typically form along divergent boundaries while composite and stratovolcanoes form along convergent boundaries. A scientist might also look for evidence of a magma chamber that feeds (or fed) a volcano.
Finally, if it is an existing volcano, a scientist would look for evidence of material ejected by the volcano. Things like volcanic ash and lapilli would indicate that the mountain in question was an explosively erupting volcano.
http://www.dartmouth.edu/~ears5/handouts/volcano_characteristics.html