After learning the grammar rules (well, the basic ones at least) try to read aloud in Russian (after hearing it in audio-version). Don't worry if something would be difficult at first.
Our memory is functioning like that - the more information channels you use - the better you remember it afterwards. If you use your eyes for reading, your ears for listening and your mouth for speaking, the progress would be faster.
And I advise you against the newspapers - they use an artificial language that is hardly encountered in real life.

Also, try to get some russian DVDs with both English/Russian subtitles and watch them twice at least. For the first time, turn on english subtitles to understand it, then turn on Russian subtitles to read what you hear, then you can try to watch the movie without subtitles at all.