Setup: I was looking at some of my dad's photos from his recent pack trip,
and he complained that they were not sufficiently sharp.  I asked some
questions about his shooting setup and provided a few options, including
that (given the very small aperture) they could be diffraction limited. He
had never heard of the possibility, so I provided a thumbnail description
of diffraction effects.  At some point, my dad e-mailed his brother, who in
turn followed up with a link: http://www.kenrockwell.com/tech/focus.htm
  I followed up with this response :
  For the purpose of illustration, I like this site:
 http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm
 (they have actual photos, and everything!)

 This site also covers some of the interactions between diffraction
effects and digital photography, which further complicates matters.

 On the Ken Rockwell article:
 Ken Rockwell is somewhat hyperbolic about his own contributions; these
are all well understood but complex issues.  The physics of the system has
largely been known and understood for at least one hundred years, but
sadly the physics is in some sense the easy part.  These issues ultimately
have their root in human perception of "sharpness", which varies between
people (distributed as per a normal distribution, naturally!), and even
once you fix a particular viewer it varies depending on viewing
conditions.

 Rockwell's advice is practically hard to apply in the format we use, and
his calculations end up being based on the total length of travel of the
lens required to focus from nearest item in the scene to to furthest item
in the scene.  His (dozens!) of pages of tables are all for different
formats, and not really directly applicable to us for couple of reasons:
most modern lenses don't have a depth-of-focus scale on the lens, and
many modern lenses have interior lens elements that move while focusing
(which completely invalidates the usefulness entire "change in lens
length" measure).

 Having said that, there is a good message here, though not one that is
hugely practical to apply.  In your scene, you want a swath to be
"suitably sharp" after being printed at some particular size and being
viewed at some set distance by a particular viewer (who falls somewhere on
said normal distribution) in a particular environment.

 To attain this desired band-of-sharpness for your scene, you magically
establish (say, using an iPhone app, a cardboard "DoF calculator",
Mathematica, whatever) a focal setting and aperture setting.  For a
point at each distance that you want to be "suitably sharp", there is
a corresponding "focus disk" (that is, the disk of light that would
result from a point source of light at that distance).  For this f stop,
there is also a corresponding Airy diffraction disk; if the diffraction
disk is larger than the focus disk, then there will likely be visible
diffraction effects in the resulting photo.

 So, as long as you have complete foreknowledge as to what size you are
going to print your photo, how it is going to be displayed, what distance
people will view your photo, who is going to look at it, what portions
of your scene are actually going to make the end photo, and can perform
the resulting calculations on the fly (or print out dozens of pages of
tables), this approach will work out for you.  (as an aside, the web site
that I linked to has such a calculator!)

 Otherwise, any time you make the aperture smaller than about f/11, you
should realize that there may be diffraction effects and try a variety of
f stops (down to about f/11).