The short answer (to the question in your subject line) is that in an explosion the skin is blown outward, and in impact damage it's (usually) blown inward: In other words you can tell the direction of the force applied by which way the skin around a break/penetration is bent, if you recover the right bits of the aircraft.
The labs start with "Boom = Outie, Crash = Innie", and they can also look at burn patterns (on the paint or as changes in the heat treatment of the metal), chemical residue (if it hasn't all washed away or been contaminated), etc.
In addition to leaving chemical traces or heat-related damage explosions also tend to be physically "messy", so there's usually some physical evidence. Shrapnel punctures through control surfaces are a distinct possibility in an explosion (those punctures generally have a different characteristic than denting and tearing from impact with rocky ground, and again if you get lucky you might even find bits of shrapnel inside the punctured control surface).
The longer answer (to the rest of the question) is that sometimes you can't conclusively tell what happened, particularly from just a single piece of wreckage like a control surface.
In fact quoting from the story you linked there are three different (and valid) theories about what could have caused the damage seen on the particular piece of debris in question:
The rear damage could have been caused if the airliner had its flaperon down as it went into the ocean, some members of Exner's group wrote in a preliminary assessment after looking at photos and videos of the component.
Entirely plausible: Impacting water at speed could tear chunks out of the trailing edge of a flaperon. It could also break the control surface free of the rest of the wing.
But the lack of damage to the front makes it more likely the plane was in a high-speed, steep, spiral descent and the part fluttered until it broke off, the group said.
Also plausible: Aerodynamic flutter could break pieces of the flaperon off, or tear the entire control surface from the aircraft (in which case damage may be evident at the points where the flaperon attached to the rest of the wing)
The lack of damage to the front section "tells me that the component could still have likely been back in its original position inside the wing itself,"
Still plausible but a bit more exotic: The flaperon could have broken off post-impact (and the damage to the trailing edge could have occurred on impact, post-impact, or even pre-impact while the aircraft was still flying).
Note that a lot of what's being put forth in that article (and others) is speculation based on a few photos showing only part of the debris (so far I haven't seen any showing the "bottom" of the debris). A conclusive determination can only be made when the debris is recovered and examined in its entirety.
Attempting to draw conclusions without the full picture can lead to interesting results: The apple is perfect until you see the other side.
