So, this is based purely on trying to recreate the look in the picture that you posted, so I'm not sure if you're only looking for a tutorial on that or on negative images in general, but hopefully this helps.
My first step was actually inverting the sample picture that you provided to see what it would look like in the positive. This presented a mostly greyscale and desaturated yellow picture. The other thing I realized was that if you invert blue, you actually get orange, hence my theory that the blue has been desaturated.
Here's the before and after:
1. First, I created a new hue / saturation adjustment layer. I desaturated both the blue and the cyan to -100. I then desaturated the master colour to approximately -35. This kept some of the colour, but made it more muted.
2. I merged the layer down and inverted the image using Ctrl + I (or Apple + I if you're using Mac).
3. This created a close approximation, but I then created a new levels layer and moved the grey point closer to the white point.
4. To finish it off, I used the burn tool on the cloud highlights to darken the clouds a little bit.
I realize it's not perfect, but that kind of gives you the basics, and with these steps, hopefully you'll be able to work more on your own image and get it even closer.
Hope that helps
