Hello everyone.
Aspect of Russian verbs can be tricky to understand for foreigners, so I'd like to write this short introduction into Russian aspect system. Many books and online lessons focus primarly on formal grammatical rules and lack the explanations of the internal language logic that manages all the rules to run together. I think a small overview of general ideas would be helpful.

And of course, as my English is not pretty good, any your corrections of this article are highly welcome.

As you probably already know, there are two aspects of Russian verbs: perfective and imperfective. Many verbs go in pairs where both verbs have the same lexical meaning, but differ in aspect (нарисовать — рисовать, спеть — петь, встать — вставать). However, there are a lot of verbs that go without pair, perfective (грянуть, зашагать, очутиться) or imperfective (спать, принадлежать, разгуливать).

The meaning of Russian aspect are completely different from the meaning of Progressive Aspect or Perfect in English. If you try to find some mapping between usage of Russian and English aspects, you'll fail to do that. Instead, you should learn to see the world through the eyes of Russian language.

Every verb describes some situation. What kind of situations can it be? The major division is by events and processes. And that is the same division which corresponds to perfective and imperfective aspects. All the perfective verbs are events and all the imperfective verbs are processes.

Well, you should note the important thing: subdivision into events and processes do exist only in our mind and not related to anything in the real world. The very same situation can be viewed as an event or as a process depending on the context and intention of a speaker. Most of the situations we can think of can be viewed as either event or process, that is why many verb go in pairs. However for some situations, decribing them as events makes no sense. These situations correspond to imperfective verbs without matching perfective pair: принадлежать (to belong), иметь (to have), спать (to sleep) and so on.
Perfective verbs without imperfective pair also exist, but that seems to be due to grammatical reasons. For example the perfective verb очутиться (to find oneself somewhere) theoretically can be transformed into imperfective очутиваться, but it sounds awfully ungrammatical. (But its very close synonym оказаться has matching imperfective оказываться, so that has nothing with lexical meaning of the word, but some internal grammatical restrictions.)

Let's take closer look at events. From the point of view of the language, event is always something instant; event cannot have any internal structure and its actual duration is not very important. In the real world some action can take a moment or ages, but if you think it as something solid, it is an event and we use a perfective verb for it.
Another significant feature of event is that it always involves change of some state. All perfective verbs mean "some state changed instantly", so if you don't think of state changing, you shouldn't use a perfective verb.
For example perfective verb прочитать mean "to read something completely", so if you say you прочитали a book, it actually means you read the book completely and the state of your mind changed: now you know all the contents of the book.

At this moment, you maybe think perfective verbs are somewhat like English Perfect. So I should explain they differ in two significant ways. First, Perfect is used only when some result of an action is still actual. On the other hand, perfective verbs do not impose such a restriction. Even if the result is already fully non-actual and out of date, we use a perfective verb just because the result was reached at some point in the past. (If a speaker need to clear if the result actual or not, he or she has to use some additional words such as adverbs, particles and so on.)
Second, Perfect by itself does not specify what kind of result it means; depending on context (and common sense of a speaker) result may vary. But Russian perfective verbs always have concrete, specific kind of result "hard-wired" into their lexical meaning. You have to choose a proper verb from some similar verbs depending on what kind of result you mean.
So, English Perfect is about having some result, but Russian perfective verbs are about to have concrete kind of result.

Most common kind of perfective verbs are such those mean some action completed with specific result. However, as I said above, perfective verbs can express any kind of state change. Thus, there are a lot of perfective verbs expressing idea of something starts or begins: запеть (to start singing), закричать (to start screaming), взлететь (to take wing) and so on. Also, there are verbs that do mean state change but we cannot say they express some action started or finished. For example, such are already mentioned оказаться и очутиться, both mean "to find oneself in some new or unexpected state or location".


[to be continued]