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Look for Inigo Quilez articles
Good luck

I've written some blog posts on this: http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/
There are also links to Hart's and Quilez's excellent papers there.

May i explain in very simple words ?
You probably know what i'm going to say but.... just in case 

By using raytracing you assume that you can calculate directly the intersection between a ray and a primitive (eg : triangle).
However, this is not always possible to calculate directly this intersection.

That's why there is raymarching.
you launch a "ray", at every step you use a Distance Estimator (some kind of black magic function) that estimate the distance between the actual position of the ray and the closest surface of all objects in the scene, and advance by this estimated distance multiplied by a factor < 1.0 and do it again 'til you consider you're close enough to the surface of the object. (at this stage you can calculate color, reflection, and so on).

One of the others advantage of raymarching (beside the fact that it "just" works) is that some stuffs like Ambiant Occlusion is almost free to compute.
Simple, huh ?

and a picture worth a thousahds words, so here it is :
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And as said : Look for Inigo Quilez articles and good luck

How do I go about making (or at least learning about) the "Black Magic Function", the Distance Estimator. I'd like to get into rendering code, and I feel like I mostly understand how Ray Marching works now, but figuring out the closest surface is beyond me. Even if I have a REALLY simple scene, like one cube and one sphere randomly in front of a camera, how do I determine the closest point to where a ray currently is?