I've never actually done it myself, but I believe this would be a simple case of masking.
Take your footage (I'll use this:
Take a picture of a crater (I'll use this:
and composite them together. Quite simple, really. It's just once you get into moving camera and the such that you might have to do some manual motiontracking, but I don't think it should be a really big deal.
Anyway, what you need to do is place the video of your scene one the timeline, then the picture of the crater below
it. Then, mask out the part of the scene (aka layer 2) that you want to become a crater.
Then, animate the picture of the crater so it looks as though it's natural. Colour grading can then be applied to make it look as though it was shot at the same time. Here is my (very quickly done) final result:
I hope this helps you!