does the word order matter very much in russian?

There is a 'standard' word order in Russian, but the main thing is that you use the different cases, of which there are seven, correctly, i.e. the noun and adjective endings. The word order only really affects the emphasis of what you are saying rather than the entire meaning, and there are only a few instances in which the word order in russian is pretty much fixed.
Because Russian is such an inflected language (inflected = uses a case system, like latin or german), the word order doesn't matter very much. In english we rely really heavily on word order to know how the different parts of the sentence relate to one another, but in russian because the endings of nouns and adjectives change depending on their function in the sentence, that can be moved around without the meaning being distorted as it would be in english.