I'm about to start work on my game engine, but I've run into some problems while figuring out how to make it work. I'm thinking of having a set of functions such as DrawCube, DrawSphere, etc... to make drawing much simpler, and maybe some functions to dynamically change textures on the fly. I'm using Direct3D, so all this isn't that difficult. My main question is, how do I go about loading level data? How would my level files (which I haven't thought about yet, hence the reason I'm asking) be formatted and translated into on-screen geometry?

There are many ways to go about this, and nearly every game uses a different method for storing and drawing levels. Assuming your game is 3D, you can come up with a file format that basically tells the computer how to draw your level.
Something like this:

mylevel.txt


All your program has to do now is go through the level file and do what it says. So when it reaches the line "Cube: ...", it calls the DrawCube function with the supplied data, and if there is a collision detection system it passes this information to that system so that it becomes "aware" of the cube.

This is an extremely simple example, your game will probably require a more sophisticated level format but the general idea remains the same.

Thanks for your assistance, I'll look into implementing that into my engine.