What methods exist to detect airframe icing, and how do they work?
There are a few ways to sense ice on an airframe. The DOT has a document here that outlines the various types of sensors. 

First and foremost planes have ice lights that project onto the wings so they can be visually inspected. 

There are completely optical sensors that use a variety of methods to detect ice.  

There are also some electro mechanical devices, here are a few examples, the rest are outlined in the DOT document. 


  Penny and Giles
  
  The Penny and Giles system uses a probe type sensor that measures ice
  buildup in terms of Liquid Water Content (LWC). This system was
  designed specifically for use on helicopters and is available for all
  turbine-powered helicopters.
  
  Rosemount 
  
  The sensing probe is driven magnetostrictively to vibrate at its
  resonant frequency of 40,000 Hz. As the ice detector enters an icing
  environment, ice collects on the sensing probe. The added mass of the
  accreted ice causes the frequency of the sensing probe to decrease in
  accordance with the laws of classical mechanics.
  
  Sunstrand
  
  The Sunstrand system uses a mounted probe with a sensing surface
  facing the airstream. Beta particles are released from a Strontium 90
  Radiation Source and are collimated by a specially shaped window in
  the probe housing. These particles pass across the sensing surface to
  a Geiger-Muller tube. High voltage is applied to the Geiger-Muller
  tube to enable it to detect the radiation emitted by the Strontium 90
  source. Ice accretion on the probe decreases the beta particles
  detected by the tube. When the particle count drops below a pre-set
  level, a pulse rate discriminating amplifier energizes an icing signal
  visible to the flight crew. At this time a heater inside the probe is
  activated, the ice is removed from the probe, and the probe is ready
  to begin another icing cycle.


Some of these will work in a static situation while others may require the passage from a non icing environment to an icing situation.