There is a way to learn to read Russian in a very short period of time. Not being able to do it in months or days, but in hours. Far faster than you probably thought possible. But we have to be clear, here, exact what we mean by reading though: Do we mean, to sound out the Cyrillic letters in a word and pronounce them out loud so that a Russian speaker understands us?
Or do we mean, look at the printed Russian word and understand its meaning, even if we'd have trouble pronouncing it? Those are different skills. Both are easily attainable, but the first requires audio supplement. Since this article is in written form only, we will concentrate on the ability to decipher meaning. This will let us read Russian signs, for example, or surf the Russian internet.