I was looking at MARY POPPINS (yes, again) and found a perfect, simple scene with which I can demonstrate the process.
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The first shot is Bert and Mary Poppins together. Most of the B/G is obscured.
In the last shot of the scene, Mary rides off, giving us nearly 2/3 of the entire B/G.
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In Photoshop, I take this, layer it on top of the first, and erase the right third. The result is a great image of Bert, and most of the background art restored.
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Since Bert stays in place through this scene, I was unable to digitally erase him, but this still concisely illustrates the recreation process.
It also makes a point of the difficulties... if a character doesn't move, there's no way to re-assemble the entire piece! And often, it takes several little pieces, stacked in Photoshop layers, to recreate the B/Gs. Sometimes upwards of 20 layers!