I have posted an old copy of my "Guide to Gwoyeu Romatzyh Tonal Spelling of Chinese".
This document was composed in 1995, revised in 1998, and rescued by Jeffrey J. Hayden around 2002. I no longer have the original file, but what is here seems basically correct. I may revise it at some time in the future, though. In the mean time, copies and parallel versions may be found around the Internet.
Gwoyeu Romatzyh (also known as GR) is most closely associated with the name of Y. R. Chao 趙元任, even though it was supposedly the product of a committee and even though the original inspiration for tonal spelling seems to have been Lin Yu-tang's 林語堂. There is no question, however, that in its present form it is largely Chao's work. It is a finely crafted system of romanization that shows his handiwork and insights in many places.
The key idea is that tonal distinctions are represented in the spelling of words, rather than by diacritics.