I acquired a fairly good grasp of Russian grammar in a traditional classroom setting years ago, so I can’t vouch for input-focused methods for it in the way that Steve can. I have to think some study of the case system, etc., as an exercise, must help. (The little bit of Finnish you see in my banner is from my timid first steps to test input-focused methods on an unknown language with complex grammar.)
In the sentence giving trouble here, good understanding of Russian grammar does make the sentence clear. Probably you’ve got the analysis below under control already, but here it is in minute detail for whoever might benefit.
The core phrase has a subject, a verb, and an object. In the Russian example we find these words presented in this order and in these grammatical forms:
евреев – noun, plural accusative/genitive
выбрал – verb, singular past active (i.e., takes a direct object in the accusative)
Гитлер (и его сторонники) – noun, singular nominative
In Russian the subject is nominative, the verb agrees with the subject, and the object is accusative. Therefore the only possible English word order for those elements is:
Гитлер и его сторонники выбрал евреев.
Hitler (singular nominative) [and his supporters] selected (singular past active) the Jews (plural accusative/genitive).
English relies on the word order since it overwhelmingly does not change the form of the words. It’s the opposite in Russian – since the words by themselves tell you pretty much how they’re used in the sentence, the order that they’re used in the sentence is largely irrelevant. Word order can be modified for emphasis and color (much of which is beyond my level), but the basic parsing of the elements remains the same based on those word forms.
Sure, you’re not going to stop and diagram sentences when a native is yammering at you a-mile-a-minute. But continued exposure will make it easier and easier to handle sentences with non-English word order. In the long run, a fully inflected grammar like Russian’s actually makes it easier to unravel long, convoluted sentences, as well as to remove ambiguity in many instances.
Note & question: In English for “Hitler and his supporters” we would use a plural verb – which would only be apparent in the present tense – but in the Russian here the verb is singular. Is it always so in such a construction?
PS: Thank you, Mrs. Brandt, for making me learn sentence diagramming in 7th grade!