Learning the Cyrillic alphabet

What is the fastest/easiest way to learn to read fluently the Cyrillic alphabet (language doesn't really matter, but assume Russian if it helps).

It would feel badass to be able to at least read the titles of books in the Russian section of the library.

ahem, ima russian myself and i cannot understand... i learned latin alphabet at school without any problems and as i remember we had only few lessons for it. moreover i've never seen any russian who complained he couldn't read latin letters. i wonder why do foreigners have problems with so close script, i guess they could learn it after after couple of hours