Hit up the site, enter the lyrics you know (or think you know) and click search. LyricRat will return the result, as well as some possible alternatives, along with the album info and even a sample of the song (all linking to Amazon). The site does well with lyrics commonly mistaken, too; we tried the commonly misheard lyrics to the song in the screenshot and LyricRat still got it right.
What sets LyricRat apart from other search engines or even just a Google search is the ability to tweet your lyrics to @LyricRat and get almost-instant results with a link to the page on LyricRat for the full information.
So while Google is still probably your quickest and easiest option, LyricRat is a fair alternative, especially for quick results on your mobile phone via Twitter.