You need a program with layers. Photoshop, Gimp, etc.
Then you open a new image and copy in the base image, on a new layer you paste the next image you want and set that layer to a mode - multiply, screen, overlay etc. so it's not a solid image and then you can adjust opacity a bit.
Then repeat doing that until you're happy with how it looks.
No, for making images like the one you linked Paint is pretty much useless but there's Gimp which is free to download and use or Sai which is also free. Both have layers and modes etc. and you could easily make images like that one with them.
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