A more advanced way of making a selection and extracting images is to use the Pen tool. The Pen tools is more a way of working with vector shapes, and let's us get some really nice curves. It's a lot more useful than using the marquee selection tool for smooth selections/extractions.

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In this demonstration, we will extract this boy's face from the background using the Pen tool:

We can either use the Pen tool or the Freeform Pen tool. The difference is that when working with the Pen tool, we choose when to place our anchors, but with the Freeform Pen tool, it will 'guess' where is the best place to put the anchors - you can alter the settings by using the magnetic options for example.
First, we will try the Freeform Pen tool. We can zoom in for a better view, but make sure the whole image is still visible to you - particularly if you're using magnetic, as it will prove difficult to move around whilst drawing. Try to draw down the side of the face. With magnetic turned on, it can be a lot easier:

Selecting around the edges with the Pen tool doesn't matter, as we can easily add that to the selection afterwards. The main aim of the Pen is to separate the background from the part we want. We can use the Freeform Pen tool to select the Path that was created and examine the curves. We can also edit the Path to make a better fit. Using the Freeform, you can hold Ctrl and click to move anchors around, and hold Alt down to edit the anchors's curves.
For example, here where the path doesn't get close enough to the mouth, we can add a new anchor at that point by simply clicking on the path (notice the cursor changes to a Pen with a + sign:

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Now choose the Convert Point tool and move the new anchor in to the lip:

Next, we can use the same tool to move the arms of the anchor, to change the direction of the path to match the face:

Now go around the path and make sure it's snug against the face - adding, editing or subtracting anchors as needed. We should have something like this:

Now we can goto the Paths panel (Window > Paths), and then right-click the path we created in the panel, and choose Make Selection, 0 Feather.

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Now we can fill in the selection around the edges with the regular marquee tool, and then copy and paste into a new layer, and do what we want with the background (blur, for example) or give it a new background:

Notice how smooth the edge is - a selection marquee tool alone could never achieve these results.

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