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An HDR effect is a simple way to give a dramatic slant to an ordinary picture. There are lots of possible ways that you can replicate the effect but perhaps the easiest just relies on duplicating layers and setting blend modes.
Start off with your original layer and duplicate it twice. With the first duplicate, desaturate by pressing Cmd/Ctrl+U. Change the blend mode of this layer to Overlay. With the second duplicate, simply change the blend mode to Soft Light and reduce the Opacity from anywhere between 50 and 80%.