The simplistic answer is:

Extratropical systems are asymmetric with winds well away from the center and the center generally exposed. They tend to look like a single spiral that rarely wraps more than about 1/2 to 3/4 around. A nor'easter is a good example of an extratropical system. These generally form over colder waters.

Tropical systems are symmetric with a tight inner wind maxima and clouds all the way up to the center (excluding an eye). Due to the dense CDO, weak systems tend to look more like a single spiral, but more powerful systems develop a clear double spiral. These generally form over hot waters.

Subtropical systems are sort of half way between these too. They generally have the symmetric structure of a tropical system, but the winds are well away from the center and the center is sometimes exposed. These generally form over medium temperature waters.

Wikipedia info:
Extratropical: http://en.wikipedia.org/wiki/Extratropical_cyclone
Subtropical: http://en.wikipedia.org/wiki/Subtropical_cyclone
Tropical: http://en.wikipedia.org/wiki/Tropical_cyclone

I'm sure a met can give a much more detailed description, especially of exactly how to tell subtropical from the other two.