When we have a photograph that we think will look great in Black and White, we can turn to the quick and easy method that Photoshop provides. It is available from the Image, Adjustments, Desaturate menu option. Take this photograph of a flower:

Going down this quick and easy route will give us a perfectly reasonable Black and White photograph:

We can, however, gain much more control over the way our Black and White conversions are being produced, and it can result in much better images. Before we do that, lets quickly think about how Photoshop might be converting to Black and White. Essentially, Photoshop is just simply losing colour information and calculating the grey value based on the average of the colour components. What if we were to control what bias is made over the different colour components of an RGB image?
The way we do this is through a Channel Mixer, and we can get one of these as an Adjustment Layer.

Here's what its dialog box looks like. Note, for this tutorial, we are going to check the Monochrome option in the bottom left:

Now we can drag the RGB sliders to change the proportions of what goes in to the final grey image. To gain a similar result to Desaturate, just pick 33% in each channel. Note that the dialog box shows you the total output. When mixing, try keeping the total output 100%, although this can be ignored if you really want.
Here are images created with 100% of Red, Green and Blue respectively with the other colours 0%:

 
For the final image, I created two black and white versions of the tulip, one using 100% red, one with 100% blue, as two layers, with the red layer on the bottom, and the blue layer on top, with the top layer's blend mode set to 'Multiply'. Compare this image (left) with the ordinary desaturate (right):

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