Isn't this question a bit like asking "What's the fastest way to paint a picture?" The answer is probably "Badly".

The real question, for me, is how to learn a song so that you really know it; so that you can sing it in a way that means something (and so that you can sing it without having to read the words off a bit of paper, which I have always thought of as disrespectful to the song itself, not to mention any audience who have to wait when you lose your place – but then I'm probably a bit weird!)

My own method: I just keep singing it over and over until I can sing it without any hesitation and can sing it whilst doing other things: walking, driving, cycling (you do tend to swallow a lot of flies!), washing up etc. Some songs come quickly and I can usually sing them without prompts within a few days but I always wait a month or so before inflicting them on others. If a song doesn't come quickly it means, to me, that it's not for me and I shouldn't try singing it in public.