The only way I am aware of is trying in many different systems as possible. I doubt there is a program or formula you could use as there is just too many possible combinations or graphics cards, ram, ram speeds, bus speeds, clock speeds, etc., etc.

One way to figure out the minimum memory required for your application is to obtain free memory from the system before starting your code and later when you allocate all the memory required, doing it again. The diffrence will be approximately the amount of memory your application needs. However this is not very good solution it is easiest one. The another would be to use custom memory manager in your code to monitor every allocation and deallocation of memory and to perform final report. This way you can get more accurate result.
Other requirements are a matter of "horse power" your code needs to run smoothly. This is application specific and you can estimate it by testing your code on diffrent machines. The more the better.