Here I'm simply getting the selection of the layer that will be the foreground element (the 'woman' in human terms). Select with the magic wand tool (look at the toolbar) and then right click and select inverse to close the selection in on the forward anomaly.
Drag the anomaly into the open document that you want to use as the background.
Now go in and finish the selection by the magic wand tool and right click to choose similar. This will allow the selection of similar colored pixels on the layer. You can then go ahead and edit: cut.
Feathering a selection before you cut will make the edges smoother. In this case you'd use a very small feather ie. 1.
Now select the entire layer of the anomaly (enough with this anomaly horsecrap.....it's the size of Texas Mr. President..). You can do this by Ctrl/Cmd clicking on the layer icon to get the marching ants.
Now create a new layer and press Alt/Opt Backspace to FILL the selected area with your foreground color of black. It is vital to have the area selected, otherwise a fill would cover the entire document on a new layer. We are creating an exact selection and 'filling' it with black to form a custom shadow. Wait until Peter Pan hears this.
Now, go ahead and create a layer mask on the SHADOW layer. We are going to be masking to hide the black dark pixels to let the original layer show through. Simply creating a shadow effect. Just mask the areas of black using the gradient radial tool with black as the foreground color. Please don't let the black confuse you as it did for months with my dimwitted mind. It gets worse when you have to remember to use white on the black layer to bring back the black and if you're really new the red rubylith will make it worse! Hehe. Just remember that black as the foreground color will HIDE pixels on the layer mask. White will BUY BACK your original pixels (whatever color they may be). Oh, and remember to do your masking ON the layer mask (selected in the layers palette) and click onto the layer icon when you're done.
You can also create another copy of the original anomaly (sorry ;) and do some adjustments such as levels or a lighten group blending mode to make it brighter. Then we can mask areas of this layer that we don't want to be seen so we can do from a portion of the face extra light to normal to shadow. Once again, layer masking is covered in depth in the Basic Photoshop DVD Training program (which comes with the Discover Photoshop: Total Package).
Here I've done the same thing to the original background layer; made it brighter and then masked the bottom right of it with the linear gradient tool to leave the upper left brighter and in more contrast.
You can also create another clone of the background layer and make this one darker (using ie. adjustment: levels). Go ahead and fill a new layer or the background layer (as long as you have an original for safekeeping) with black. This will act as night. If you can follow along and understand how to immediately apply this in Photoshop then you are doing really good.
Drag the original layer to the new layer icon and bring up levels and make a levels adjustment on the layer itself to make it lighter.
You can then add a layer mask on the lighter duplicate layer and mask (linear gradient with black as foreground color) to let the darker areas beneath show through. Here, again you see the rubylith to show the masking job.
Look at the palette as it starts getting more complicated when you have several layers using layer masks all at once and the only bottom layers that you see are the ones that are masked in certain areas on all of the layers above it. You can add some masking on this dark layer if you want pure black to show through as you can see.
The black areas where the finger is pointing to are the areas on this layer mask icon that are hidden on the 'light layer'. The rubylith that is showing is the layer mask icon that is currently 'selected' which would let nothing but black show through.
Then I went in and masked areas of the layer above it to let the "light' bleed through. So I've masked the layers to let the dark night show and then went ahead and created a white fill layer and masked most of it to hide the white leaving the corner still left.
Take a few moments and study the layer mask icons in the palette remembering that black is what is masked on that layer and white is the area that remains visible on the layer. Black on the layer mask icon will show through to layers beneath it. Try looking at it from different angles like that. I'm not using grey because I like to see things in black and white (just kidding) but it's important to note that grey is in between. Remember that layer masking works on it's own channel in a grayscale mode (you use white to black and grey in between to mask). The closer to white the grey is, the more of the original pixels will be showing and the closer to black the grey is, the more they will be hidden.
You should now 100% understand the depth and intricacies of layer masking, shadowmasking, rocket science and quail hunting. If not then be sure to get my Photoshop Designer training.