How does a typical finger stick glucometer work? What is the 
precise chemistry of the strip and does the meter measure resistance or current?
A rough drawing or link to a strip showing the layers and electrodes
would be appreciated.

All modern hand-held "finger-stick" blood-glucose meters are based on
the reaction between glucose and an enzyme that catalyzes the
oxidation of glucose (usually the enzyme called, logically enough,
"glucose oxidase").  In this reaction, glucose is oxidized to hydrogen
peroxide plus gluconic acid.

In the first generation of hand-held glucose meters, the hydrogen
peroxide produced in the oxidation reaction reacts with a a dye-based
oxygen acceptor.  When oxidized, the dye changes color, and the
intensity of the color change is proportional to the glucose
concentration in the blood.  The meter measures the amount or light
reflected from or absorbed by a dye-impregnated surface to determine
the intensity of the color change (i.e., the response is measured
photometrically).  The output of a photometric sensor would usually be
measured in terms of a current.

A newer generation of glucose meters incorporates an electrochemical
cell within the device, and measures the integrated current produced
by the glucose oxidation reaction, a quantity that is proportional to
the amount of glucose present.

The following links are to some articles that explain how blood
glucose meters work, and contain a few schematic diagrams of the newer
electrochemistry-based devices.



http://www.uspharmacist.com/index.asp?show=article&page=8_995.htm

http://www.electrochem.org/publications/interface/winter98/IF12-98-Pages26-31.pdf

http://bmj.bmjjournals.com/cgi/content/full/319/7220/1289

http://www.sciencemag.org/cgi/content/full/290/5495/1315