Let's start with a difficult image -- one that does not have a lot of contrast, so we can explore several steps to achieve the effect (all these example images are at 75% of the original size):

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The first method is to simply use Adjust...Brightness/Contrast...Threshold to do the conversion:

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That's not a bad solution, and will probably suffice for most purposes; but it can be further stylized to smooth out the rough edges and get rid of the small specks. Here's how:
1. Use Adjust...Brighness/Contrast...Fill Light/Clarity with the Fill Light at "0" and the Clarity all the way up to "127":

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2. Effects...Photo Effects...Black and White Film using the "BW Normal" preset:

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3. Adjust...Blur...Gaussian Blur with a 1 pixel radius:

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4. Adjust...Brightness/Contrast...Threshold. For this image, I used a value of "130":

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5. Use the Magic Wand to select all the black areas, and then Selections...Modify...Smooth. De-select the "Preserve Corners" and the "Anti-alias" options, and use a "Smoothing amount" of 16:

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6. The smoothed selection is still active, so use Selections...Modify...Remove Specks and Holes. Use the "Remove Specks" option for square areas smaller than "50 x 1" pixels.
7. Fill the smoothed and de-speckled selection with black.
8. Invert the selection and delete.
You'll be left with a more stylized and smoother effect:

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Now you can use various PSP tools to get the black part of the image onto its own layer against a transparent background and create a new colour layer beneath it, or copy it onto another image, etc.
Enjoy!