The first thing one would look at is if there are minerals
present that are large enough to either be identified with the
naked eye or with a handlense. Most lavas have large volumes of
extremely finegrained material or glass whereas plutonic rocks that
mostly crystallize in depths of several kilometers are usually
composed of millimeter sized minerals. Further differentiation of
ejecta can be done like (ash, lapilli, volcanic bombs,
pahoehoe-lava etc.).
One can then look at the mineralogical composition of these
rocks to define whether they are basic (little silicon) like
basalts/gabbros or acid (a lot of silicon) like rhyolites/granites.
The usual classification is the QAPF-diagram (quarz, alkali
feldspar, plagioclase, feldspathoid), which is composed of two
ternary diagrams. If quarz is present the ternary diagram including
quarz is used, otherwise the one with an feldspathoid endmember is
chosen for classification.
This field description is then usually followed by a series of
lab analyses of the chemical and isotopic composition of the rock
in order to be classified via their elemental composition. One
example is the TAS-diagram (total alkali elements versus silicon
dioxide content).