In the following table "O" means driving axle and "o" means a unpowered leading or trailing axle.

The Meaning of the UIC Wheel Arrangement (based on the german system):

Unpowerd axles: 1,2,3,...
Coupled Driving axles: A, B, C, ... [A = one driving axle, B = two driving axles, ...}
Individualy driven axles: Bo, Co, Do, ... [Bo = two driven axles, Co = three driven axles, ...]
Movable axles, trucks: '  [2' = two axle bogie, Co' = bogie with three driven axles]
Axles not in the main frame: (....)   [(2'C)C2'  wheel arangement in an articulated loco (Challenger)]
Coupled trucks: X'X'  [B'B'B' = three truck shay, all trucks driven by the same engine, mechanically coupled]
h: Superheated Steam
n: Saturated Steam
# following n or v: Number of Cylinders
v: Compound
Turb: Turbine
t: Tank locomotive

The Meaning of the Whyte Wheel Arrangement:

First Number: Leading wheels (two per axle)
Last Number: Trailing wheels (two per axle)
Numbers between: Driving wheels  (two per axle)

The Meaning of the French Wheel Arrangement:

First Number: Leading axles
Last Number: Trailing axles
Numbers between: Driving axles

Names:

Naming the wheel arrangements was a tradition only in the USA and Canada. Some wheel arrangements have multiple names, as different railroads used different names, which were not takeon over by other railroads. More exotic wheel arrangements often received never a name, as those locomotives were from countries other than the USA and Canada.