Honestly, there really isn't a short cut to this kind of thing. You just have to do it a lot. I have to learn music all the time for different things, and I find I can memorize a song fairly quickly. This has come with nearly 13 years of experience though.

What is my method? What really helps me is charting out a song; writing out the form and seeing it on paper. I know not everyone can do this, but perhaps you can develop some sort of shorthand way of writing the song form down. Try also memorizing in pieces, and not moving on until you can play the previous part flawlessly. This can be a bit cumbersome in the beginning, but through time you will be able to work through each song much, much faster.

What is a song you are currently working on? Let's start there and see if we can piece together a flow sheet of sorts to help you work out a method that works best for you.