What you are looking for is a so-called projection. And for mapping the surface of a sphere to a plane there are many alternatives, each of them having their specific advantages and disadvantages. Example are: Cylindrical, Conical, Conformal, ...
Take a look at http://en.wikipedia.org/wiki/Projection_%28cartography%29
to get a feel for the basics. Then decide, which projection would be most suited for your application. To write the code for that projection is usually the easiest part and more or less straight forward.
Ok, cylindrical is what you like. That is an easy one.
(a) Map your longitude to the x-coordinate by simple multiplication by a scale factor. Choose that factor in a suitable way such that the desired longitudinal range fits on your window.
(b) Now the latitude: At the equator, the latitude is mapped to the y-axis by the same factor as you used for the longitude. But with increasing latitude, parallels must be spread wider and wider in order to maintain angular correctness. So you have to apply tan (lat) and then multiply with the same scale factor as in x-direction.