His main contention was that first and foremost you must avoid oversights. His recommendation was that while blunders can’t be avoided entirely, by applying examining a position for tactical threats at every move mistakes can be drastically reduced.
His conclusion was that one should do what he did as a 14 year old. He played over games by covering the moves with a card and then trying to guess the next move. Good annotated games help, but are not essential because what really matters is that you put in some work and then compare your move to the one actually played.
He recommended the first book that should be used for such a method was Chernev’s Logical Chess Move By Move because there are notes after every move. After that, you are ready for other books.
He also claimed that while it was good to read chess text books, they are in no way a substitute for playing over games. Reading theory helps in the long run, but don’t expect steady improvement...improvement will come in spurts as one suddenly grasps a principle. He wrote: Playing over games and solving problems from actual play...is quite different. It improves you minute by minute. You can feel it doing you good.
The idea that you could play better if only you knew the openings “is really crazy,” he wrote. Chess skill has very to do with openings and a basic knowledge of openings is good enough until you become “fairly good.”
If you feel like putting in some effort another good way at improving is to force yourself to play through games blindfold. He pointed out that when you don’t have to play over games blindfold doing so is irksome, but if you make yourself do it, it becomes easier. The reason this helps is because a lot of chess is visualization and playing over games without a board helps in this area.
Purdy correctly pointed out that positional play is necessary only when there aren’t any sound tactical threats in a position, but that is going to be the case most of the time. Let me emphasize the sound part. I have seen many players who think they are playing tactical chess simply because they sacrificed something. Many times the "sacrifice" is nothing more than a voluntary parting with material.
Purdy, writing in the late 1950s and early 1960s, recommended two books as must study ones. How to Force Checkmate by Fred Reinfeld contains 300 diagrammed positions, subdivided into mate in one, two, or three moves. It introduces you to a vast array of mate situations and you need no board.
Purdy’s other recommendation was Win At Chess, also by Reinfeld. The 300 practical chess problems are taken from actual tournament play, contain traps, sacrifices, mates, winning combinations, and exchanges that will help sharpen players' eyes. Helpful hints are given for each problem and a table of solutions and alternative moves shows players how to evaluate their attacks. The three books Purdy recommended are good even today!
An astute observation was made by Purdy when he said he had seen players go right off their game after being frequently inveigled into playing against weaker opponents. Apparently one should try to be the “inveigler.”
He advised that when playing over games you should not spend a great deal of time trying to figure out where you went wrong. Even if you understand only half of the moves you are learning something and your percentage will eventually start to go up.
For further reading see my posts Editorial On Positional Play, What is Positional Play? and Tactics, the Pornography of Chess.
Much of what Purdy recommended was later advocated by Kenneth Smith and you can download Smith’s improvement course from Dropbox HERE.
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