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.

How about resources for how to draw the characters, stroke by stroke? Childrens books that teach how to write? Examples of Cyrillic handwriting?