The idea behind razor sharpening is so simple that either everybody already knows (but doesn't let on) or it just one of those things that suddenly becomes obvious (afterwards)
Let us consider the simplest possible case of a blurred image that we want to sharpen. (actually that would be "un-blur" but the difference is pretty philosophical)
A black-white image (1) to which a blur has been applied - in this case with radius 10 (2).
Now what is the simplest way to get back to the original un-blurred image?
Well, just select half (3) and smudge towards the middle.
After that, invert the selection and smudge the other way.
In (4) the top part has been "un-blurred" and the bottom has not.
OK, so now you say this doesn't have anything at all to do with real images.
Please, hold with we - we'll get there soon.
Let's go back to our blurred image (2) and use some automated steps this time.
Here I've applied a High-Pass filter with radius 10 (5). We can observe that the darker part of this image corresponds to where we want to smudge the darker area, and the lighter part is where we want to expand the lighter part.
By applying levels we can make ourselves some nice masks. (6 - dark mask) & (7 light-mask).
Now, we need to automate our smudging. In Photoshop there are two little-used filters that will do exactly what we need here: introducing the minimum and maximum filters. (If you've never seen them look at filter>other> )
We are going to apply these (at twice the radius) to two copies of our image.
You can see that in (8) the minimum filter has "pushed" the dark area to the right and, conversely, in (9) the maximum filter has pushed the light area to the left.
Byapplying the masks we made earlier we can control the "pushed" areas and our razor sharpening is done. In (10) the top half is the "after" and the bottom is "before" (well, that ought to be pretty obvious).
Very Interesting Stuff
OK, so what about real images?
The idea is just the same. All you need to do is to choose a radius that corresponds to the blurring of your image. Zoom in on an part that is clearly blurred (clearly blurred?) and estimate / measure how many pixels are involved in the transition from one area to the other (i.e the width of the blur). Use half of that for your radius.
Or, if you just want to make an already good image even sharper then just use a radius of 2 or 1 - but be careful or you may cut yourself (on jaggies).
Here is an image (11) that I borrowed from an art thread - not really blurred at all.
But a quick razor-sharpening (12) and the subject really "pops".
Hope you managed to follow this.
If all this seems like too much hard work, then just use the action is in the accompanying thread.
Now you be careful with that razor!!!!