There are quite a few different ways of doing this. I have to say "it depends" because if you are producing a desktop only app you might be thinking of making a windowed app, if you are aiming for mobile then you probably need more of a catch-all method.
For mobile I tend to decide whether the height or width of the screen is most important and size all sprites based on that height. Also you might want to consider sticking with a set "virtual" resolution.
For example I might create a landscape side scrolling app and decide the height should remain constant at 600. Then I'd calculate the width based on the display aspect IE:
SH = 600
SW = (GetDeviceWidth()*1.0) / (GetDeviceHeight()*1.0) * 600
SetVirtualResolution(SW, SH)
There are so many different "but if" possibilities you will have to feel your way for a while before it clicks.
Hope that helps a little!
Using AppGameKit V2 Tier 1