Here is part of an old dialogue written to a friend:
Keep in mind that different grammarians or linguists use the term Aktionsart in bewildering and disparate ways. But older grammars often employ Aktionsart as a reference to action that is delineated by the verbal stem.
Stanley Porter points out that K. Brugmann (in 1885) was the first writer who employed the German term Aktionsart to describe: "the kind of action indicated objectively by the verb" (Verbal Aspect in the Greek of the NT, Stanley Porter, 29). So when I talk about "kind of action" in this context, I mean action in terms of completed, durative, ingressive or conative (inchoative) activities that are objectively signaled by the respective verb stem (root + affix) or in some other fashion.
For example, K.L. McKay (when discussing the conative and inceptive use of the Greek present "tense") provides an example from Jn 10:32:
DIA POION AUTWN ERGON EME LIQAZETE: "for which of these deeds are you trying to stone me?"
McKay thinks that the present verb LIQAZETE in this passage, "has the effect of so emphasizing the incompleteness of the activity that the most natural English equivalent is try to do" in this case.
So in Jn 10:32 we evidently have an example of the conative present. Certain scholars would argue that the conative "kind of action" is signaled by the verbal stem (Aktionsart). Others would contend that we know LIQAZETE is conative present (imperfective aspect) in view of contextual features that mark the action of the verb (still referring to Aktionsart). I hope the example from Jn 10:32 helps you to see how Aktionsart is applied by graammarians and linguists.