Now that I'm home - thats almost exactly the book I have. In fact, here's the 1984 version...
http://cgi.ebay.com/National-LOGIC-...lectrical_Equipment_Tools&hash=item1c115c32f1
Did some searching and supposedly at one point they were offering the books free or pretty cheap, and I also found this..
http://www.national.com/JS/searchDocument.do
Which is pretty good for quickly looking up a datasheet if you keep a laptop nearby, but honestly the book is nice because it can be right there.
More datasheet links:
http://www.libraries.uc.edu/libraries/engr/databooks/index.html
As for what to do, or where to start, I think thats half the battle. Get the manual/service manual/schematic for the board, and go from there. For a watchdogging processor - do the watchdog bypass and see what happens. If the game seems to work, its possible that something in the actual watchdog circuit is bad. If it still doesn't work, then work your way back from the watchdog. For example, on a 6502 processor, pin 40 is the watchdog. Its an active-low watchdog, meaning, when that pin goes LOW, its watchdogging. When its high, its working. From there, trace that back to what does the watchdog, and figure out why its going low.
Now that said, I spent a lot of time doing exactly that on my video pinball board (again I'm a newb to this stuff), and what that really provided was a good lesson on using a logic probe and how a watchdog circuit works. In the end, I realized I had no video, started at the end (video) and worked my way back and quickly found an actual issue. I had no video, checked the chip that provided the video, found one of the signals its supposed to get was stuck high, traced that back to a different chip, found the chip was working except for that pin, replaced it, and now I have a picture again. (although still not 100% fixed). Just an example but sometimes you need an example to get a grasp of this stuff. I wish I could just watch someone who fixes these things for a living troubleshoot a board one day, just to see their train of thought.