Map of... uh... nameless world

[sirdanilot]

Okay, this is going to be a bit hard to explain, so bear with me.

1. The north south distance of my map is X degrees (I have to decide this still, but not that hard to do), and the entire world is in total 180 degrees from Pole to Pole (like our earth). I would apply a grid to the globe (also choose a meridian line and applying the vertical grid lines), and then determine the coordinates of where my map is located. For example, if my map is like 40 degrees from north to south, and I would want it be located on the southern hemisphere, I'd choose the north end 10 degrees (north), south end 30 degrees (south), and some random position on the east/west scale.
2. Now this is what I want to ask: how would I parse my FLAT map into the coordinates I determined in (1)? It would require folding the map so that it can fit a part of the surface of the globe.
3. Then after doing that I would want it projected back to 2d for practical applications, but I'd be happy with the first two steps.

I hope I am making this clear, since it's very hard to explain and understand.

edit: this tut shows maps of what I want it to sort of look like (almost an impossible goal, I know...)
http://www.cartographersguild.com/sh...mp-Illustrator

It seems very hard, and also uses programs I don't have (illustrator) so I do not think I can use this tutorial.

@Aenigma: thanks! But what is wrong with the rivers since I did try to make them realistic? Are there too few in the inlands? Are they too curvy?
I took care to let the rivers run from high to low, and not unrealistically such as from sea to sea (which is impossible as far as I know.