First off, it doesn't have to be Mod Podge. The first time I saw this technique done it was with regular acrylic gel medium, which you can pick up in any art or craft supply shop. Mod Podge is a water-based version of the above, translucent when wet but clear when dry. I think it's usually used by crafters as a finish or glue. It was what I had on hand when I tried this technique for the first time, but I'm by no means wedded to it, when this jar runs out I'll probably use a bog-standard gel medium.
In essence the technique is quite simple: print an image onto transparency, paint it with gel medium, transfer the image onto the new surface. The key thing to remember is that none of this is set in stone, I experiment with the technique almost every time I do it, trying new variations and mutations at every stage. You should too, it would be boring if we all did it the same way.
So first off I print an image onto transparency film. The film I use is the stuff you can buy in office supply stores for printing overhead transparency slides. It's designed for inkjet printers and has one side slightly rougher than the other so that the ink sticks and dries (I've seen people do this technique with the write on/wipe off film, which doesn't dry, and the results are quite different, but interesting too).
You can use anything you like as an image. I use my photographs, which I scan from negatives, but really, the world is your oyster. Gank images from the web, scan stuff from magazines, knock out something in MS Paint, whatever. I use my black and white photos, scanned in and resized in Photoshop, and then printed onto the transparency at whatever size I wish to transfer. I tend to print in greyscale, using the colour cartridge in my inkjet printer, so while I get a b&w, high contrast image, the image is printed in colour inks. That’s how I end up with the cyan/blue transfers I like so much. Remember to flip the image, especially if there's any text you want to be read the right way around.
After the image has dried I paint on the Mod Podge using one of those cheap foam brushes they effectively give away at the craft store. I've tried other applicators but these brushes gave me the best coverage. Put enough on so it's well covered and wet, but not so much that the receiving surface will slide around. I've seen other people paint the receiving surface rather than the image, but again, each to their own. Experiment.
Then press the image to the receiving surface, or vice versa, and burnish. Burnish is just a posh word for rub hard. Use the back of a spoon, your thumb, a hankie, a bone, your nose. whatever's on hand and works. Rub hard for a 'perfect' transfer, or be wimpy about it if you like the distressed look. Leave it for a minute or two and then peel away carefully. With a bit of luck the medium will be transferred to the new surface along with your image. With a bit of experimentation you can get to have a lot of control over how well the image takes, leaving just the right amount of distress.
And that's it, pretty much. You can use all sorts of things as receiving surfaces: paper of various sorts obviously, cardboard, cloth, canvas, old bits of wood, found objects, you name it. I've been playing around with preparing the surface with paints and charcoals and so on, and there's plenty more fun to be had in that area.
Is it archival? Probably not, and almost certainly not the Mod Podge, which is water-based. But then I like the distressed look, and further deterioration of the image over time might just be a good thing. I don’t know yet, but I'll be doing some experiments to find out.