Grayscale conversion using a Gradient Map
Using a Gradient Map to convert an image to grayscale is quick and almost always gives good looking results.
Step One: Hit D on the keyboard to set the default forground and background colors.
Step Two: Click on the New Fill or Adjustment Layer icon at the bottom of the Layers panel and choose Gradient Map...
In the Gradient Map dialog click OK.
Compared to an "Image > Mode > Grayscale conversion" the result will most likely have better contrast and will look less flat and more interesting.
For even deeper blacks double click the Gradient Map adjustment layer,..
then click on the gradient to open the gradient editor.
Move the black Color Stop to the right. You can also control the highlights in a similar way by moving the white color stop or control the midtones by moving the Color Midpoint.
Sometimes the image is too dark after applying a default gradient map. In this case click on the black Color Stop and change its color to a gray value below 100%.
If you accidentially add color stops just grab and throw them out.