"How do you determine zoom of a DSLR lens. What is the difference in zoom between an 18-105mm and an 18-200mm lens?"
>Example pictures to be added soon<

On a standard entry level to prosumer "crop sensor" DSLR, A 35mm focal length lens is about what your eye see's 
Older SLR film camera's and "full frame" DSLRs,a 50mm focal length provided this natural zoom and this has to do with the optics hitting a smaller sensor.

Focal lengths below 35mm (like 10mm) are wide angle lenses because they are wider than your natural perspective.
Focal lengths above 35mm are telephoto lenses provide more zoom than your natural perspective

A focal length of 18mm:
18mm/35mm = 0.5x natural zoom (2x wider than you see)

so 200mm/35mm = 5.7x natural zoom. When the resulting picture is blown up, the objects in the picture will be 5.7 times larger than you saw with your own eye from the vantage point the picture was taken.

105mm/35mm = the picture will be 3x what you see with your eye.

The "zoom range" is determined by the max focal length divided by the min focal length.
200mm/18mm is the total zoom range providing 11x zoom

105mm/18mm is the total zoom range providing 5.8x

This notion of zoom is how point and shoots are marketed because they have lenses that are centered around standard 35mm focal lengths.
This notion of zoom doesn't work well with DSLR lenses that have ranges outside of the 35mm natural length like 70-200mm.

There is a LOT that goes into what makes a lens "nice" beyond these numbers... F-stop and MTF accuracy charts... 

(Much more to come as time permits)
Subpages (1): Lens_progression