The following is a list of some of the most popular model train scales used in model railroading:
G scale: (1:22.5) commonly used for garden layouts. Also called LGB scale. If you like working outdoors, doing real landscaping and gardening, this is the most likely model train scale you'll want to use.
O Scale: (1:48) The locomotives are big and impressive and are a favorite of young and old "kids" alike. The 2-rail version runs on DC current. The O scale trains tend to dwarf the scenery unless you have a very large room for the layout, but they sure are fun to run!
O27 Scale: This is also 1:48 scale, but the difference is in the tighter curves. (O27 track sections will make a 27" circle compared to the standard O scale track sections which will form a 31" circle.) Also, O27 rail is a little shorter and thinner than standard O scale. Lionel is the primary, or at least the most famous, manufacturer of O27 these days - most, if not all, produced in the 3-rail version running on AC current. Lots of accessories are available with working parts (circuses, sawmills, etc).
S scale: 1:64) Not as popular as some of the others but definitely growing as a home for a lot of followers and offspring from the American Flyer era. This was my first model train as is the case for a lot of "baby boomers", and permanently instilled my passion for model railroading.
OO Scale - (1:74) Primarily used by British railroad modelers. Most manufacturers of OO scale will fudge a little on the gauge so that the locomotives and rolling stock will run on HO track. Check out the British Railway Modellers of North America for more information.
HO Scale: the most popular scale - (1:87) or 1/87th the size of the real thing. Not too big. Not too little. Fits on a 4x8 foot piece of plywood fairly well for a nice small layout. Also you'll find more supplies, equipment and accessories made for this model train scale than for any other.
TT Scale (1:120) has only a very small following in this country but available if that size meets your needs the best. Might be difficult to find suppliers.
N Scale: smaller than HO scale - (1:160) or 1/160th the size of the prototype. Also very popular because you can create a greater model railroad empire in a smaller space than with HO. If you like a lot of scenery with long trains curving around inside an interesting landscape, this is the model railroad scale for you.
Z Scale: even smaller than N Scale (1:220). This scale is great for coffee tables, a nice addition to your executive desk - good for any "large" layout in a very small space. Easy to transport if you like. At least one person I know created an entire Z scale model railroad empire inside a suitcase and displayed it at various train shows! This model train scale can also be used effectively in the background of an N scale or HO scale layout for forced perspective so that it looks like you have trains or structures way off in the distance when viewed from eye level. This makes your HO or N scale layout look even bigger than it really is.
HOn3-1/2: a narrow gauge designation indicating basically that you have HO equipment running on track that measures only 3-1/2 scale-feet between the rails instead of the usual 4ft 8-1/2in. The prototypes for narrow gauge railways are usually logging railroads where sharp turns around rocky, mountainous terrain are required.
There are other model railroad scales that have been used, but these are probably the best ones to use for the purposes and scope of this site. The tools and techniques described herein can be applied to any of the above scales with minor modifications.