In Russian word order is not too important. The inflectional endings of the words indicate their role in the sentence, unlike English which relies much more heavily on word order to distinguish predicate from subject, e.g. Fortunately, it helps us English speakers that the usual word order is similar to English. As for your sentence…
What is a little out of the ordinary here is “как следует”. I think you need to take that as a unit that serves as an adjective adverb, it’s third-person singular verb notwithstanding. The robots translate it as “well”, “properly”, “to a nicety”, and more literally “as follows”. The verb doesn’t relate to any subject or predicate in the sentence – the two words can be treated as a single unit.
“вам нужно” (to) you necessary
“будет” (it) will be
“изучить” to study
“как следует” properly
“исправления” corrections
“по вашему тексту” to your text.
These parts can be moved about somewhat without changing the meaning but, perhaps, changing emphasis. (This flexibility, btw, lends itself nicely to the composition of poetry.) Here are some possible re-orderings of the same sentence with the same meaning. It might take a native speaker to opine on how (un)natural-sounding they are, but the meaning I believe is the same:
Исправления по вашему тексту как следует вам будет нужно изучить.
Изучить испрваления по вашему тексту как следует будет вам нужно.
The будет third-person-singular form of the verb here might be what’s confusing? There is no explicit third-person subject. Where in English we’ll use “it” or “there” as an indefinite subject, Russian will leave it out and let the form of the verb carry that weight. “(It) will be necessary for you to study” is phrased in Russian without the “it” which doesn’t actually refer to anything real that you can point at. (I recently raised a question about a related construct using the third-person past tense neuter form of the verb, which seemed unusual though I’ve long been familiar with the usage in your sentence.)
How is it obvious that none of the (pro)nouns in the sentence are the subject? “You” cannot be the subject, because it’s in the dative form (вам, to you). Likewise тексту is dative, because of the particular proposition that its the object of, so it cannot be the subject. Исправления could be the subject of a sentence because there’s no difference between the nominative and accusative forms of neuter nouns. However, this is plural, and the verb is singular, so that can’t be it; исправления is actually the object of the verb будет изучить.
This type of in-depth parsing is rarely necessary. One learns to understand the sense of sentences fairly easily, I think, and the structure is usually obvious. It’s never necessary for conversational speech. There are occasionally times, though, when the author of a literary work crafts a long, complex sentence, and I find myself needing to do this sort of analysis. (I’ve maintained that the declensions and conjugations make it easier to understand such sentences since the words’ forms give very strong clues to their role in a convoluted sentence.) The more one is exposed to the language, the less analysis is necessary, and I would hope that native speakers never need to stop and do this.
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