Critical speed or Mach number is the speed at which the speed of sound is locally reached somewhere along the flow around an airfoil. A supercritical airfoil can tolerate operating speeds slightly above the critical speed (hence the name), which means that a pocket of supersonic flow will show up, most likely on the upper surface. What qualifies an airfoil as supercritical is that the recompression does not need a shock, but can be done shock-free for a small lift coefficient range by clever shaping.
See this question for more.
Calculation of a supercritical airfoil is best done with a computer program which models the flow conditions around Mach 1 faithfully. Once such program would be TSFOIL. The picture below shows one result for the BACJ airfoil at Mach 0.8, and you can see that the speed on the upper surface reaches Mach 1.3.
