First, we can categorize verbs into stative and dynamic verbs. Stative verbs describe a state, dynamic verbs describe a change. We can further subdivide dynamic verbs into four subtypes by their aktionsart. Together, we have five types of actionsart:
state e.g. (atelic, durative) "know" or "be drunk"
semelfactive (atelic, punctual), e.g. "shoot" or "knock"
achievement (telic, punctual*), e.g. "realize" or "die"
accomplishment (telic, durative), e.g. "teach" or "break"
activity (atelic, durative), e.g. "research" or "run"
*Certain achievement verbs can be durative in a sense, it can take time for someone to die, for example. But the process of dying isn't the same thing as actually dying.
Telicity refers to whether or not the verb has a defined or natural endpoint. If it does, it's telic, if it doesn't it is atelic. Durativity refers to whether the verb's action takes time. Punctuality is the opposite; a punctual verbs' result is more or less immediate.
States generally cannot be in a progressive aspect, e.g. *I am knowing it, *I am being drunk. They also cannot be described with modal adverbials: *I know it fiercly; *I think it with great care; *I am tall throughly. They generally cannot appear in imperatives either: *Know about aktionsart! *Be of that opinion! *Be tall! Since they are atelic, they cannot be described with period-descriptors: *I knew Latin in three months; *It took me three hours to be drunk (note however: "It took me three hours to become drunk").
They sort of work with these if more qualification is added and a non-present tense is used: I knew Latin for five years but then I forgot everything (the present is impossible however) I will be drunk for an hour but then I'll sober up
Semelfactives are punctual, atelic and nondurative. They do not work well progressive: *?he was knocking it on the floor. They do not work with most period-descriptors: *Knock it for an year. They do work as imperatives however: Knock it! and with modal adverbials He knocked it fiercly.
Achievements refer to changes in state, and are thus telic. Their subjects thematic role is usually that of theme or patient. However, they are not really durative and therefore cannot logically be made progressive. In English, when these verbs are made progressive with "be ...ing" they actually become habitual: She wasn't getting it, she was getting awards, she was realizing new things; or prospective: She is getting it (as in: She's about to get it), the sheets are drying (or: are about to get dry).
They do not work well with most modal adverbs: *The sheets dried fiercly, ?The sheets dried too much.. They rarely work when imperative, and then only as wishful thinking: ?Dry!, Break!, die!, *Realize!. They sometimes work with period-descriptors: She understood it in ten minutes; but often not: *She died for ten hours.
Accomplishments are durative and work with the progressive: I was teaching syntax. Some work badly with certain modal adverbials: ?I broke the glass fiercly. Since their subjects are willing participants in the action (θ-role: agent), these verbs can be imperative. Their objects often influence how amenable they are to period-descriptors: ?He taught syntax in ten months but I taught the entire book in ten months.
Activities are atelic because there is no obvious endpoint to something such as eat, browse the web, or rain. They are durative because they take time however. Most weather verbs are activities but they have no agents and are thus a bit different from others. Mostly, activities can be progressive: He was browsing the web and It was raining, though other weather verbs cannot: *It was being sunny. When activities have subjects, they are agents or agent-like and therefore the imperative works fine with the ones with subjects: Browse the web!, but *Rain!. Period-descriptors beginning with in do not work: *He browsed the web in ten minutes or *It rained in ten minutes.