While I can't really speak for dogs, when it comes to horses, this would be a pretty good progression in terms of educating yourself:
I. - Overview of all the Fundamentals:
"Picking Winners" by Andrew Beyer
"Betting Thoroughbreds" by Steve Davidowicz
"Handicapping 101" by Brad Free
(The first two listed here are quite old and the examples given may be a little outdated, but the fundamentals are still as valid today as they were then. The latter is a newer book that provides a decent overview of all handicapping factors while using recent examples and DRF format.)
II. - Speed and Pace:
"Beyer on Speed" by Andrew Beyer
"Modern Pace Handicapping" by Tom Brohamer
"The Power of Early Speed" by Steve Klein
("Modern Pace Handicapping" can seem a little technical at first, but you'll get the hang of it quickly. In my opinion, and I can only speak for myself, this is the single most important handicapping book ever written.)
III. - Class
"The Handicapper's Condition Book" by James Quinn
(This book will help you gain a better understanding of the eligibility conditions for a race and help you focus on horses that most logically fit the conditions. It's a tremendous resource on Class, probably THE book regarding Class, but I found it a little tough to wade through at times - it can be a little tedious.)
IV - Physicality of the Horse
"Horses Talk: It Pays to Listen" - book and VHS tape by Trillis Parker
"Spotting the Ready to Win Racehorse" VHS by Joe Takach
"Beat the Beam" VHS by Joe Takach
(These videos give you good examples of signs to look for visually that will help point out whether a horse is feeling good/bad/angry/wants to run/doesn't want to run, etc. This is a highly overlooked handicapping factor, but if you understand physicality, you will definitely help your bottom line.)
V. - Money Management:
"Money Secrets at the Racetrack" by Barry Meadow
"Commonsense Betting" by Dick Mitchell
(The Barry Meadow book is especially great since it provides handy charts and is easy to read and understand. The Mitchell book is a little more esoteric.)
VI. - More Advanced and/or Specialized Insights:
Some suggested reading:
"Thoroughbred Cycles" by Mark Cramer (good book about understanding how horses come and go through their form cycles and how to spot when the horse is improving/regressing)
"The Best of Thoroughbred Handicapping" by James Quinn (each chapter discusses some other writers' specialized viewpoints - there's like 30something chapters, and you get a little intro to a LOT of different factors.)
"Winner's File" by Henry Kuck (Very hard to find, but it is packed with general insights on nearly all the handicapping factors, and is easy to read - each chapter focuses on one specific thing and uses detailed examples and is only 5 or 6 pages long.)
"Exotic Betting" by Steven Crist (If you want to learn how to most efficiently bet the exotics, this book outlines it for you. His 'ABC' ranking system is very good and helps reduce the costs of your pick-3s -4s and -6s.)
There are numerous other great books out there - I just wanted to recommend some of my favorites that I thought were most influential. I'm sure I missed a few on my list, though! Additionally, you can check out
www.paceadvantage.com - it's a pretty decent horseplayers' message board. A lot of sharp guys there.
Also, one other quick piece of advice - anyone who is interested in betting horses or dogs or harness online should sign up for an account with Premier Turf Club. They are the only legit U.S. service that I know of that is tied into the pari-mutuel pools, paying full track odds, that offers rebates. They don't carry some of the major tracks, however - so that may be an issue for you. Check out their website to see their tracks list. It is pretty extensive for dogs, IMO.
www.premierturfclub.com
Hope this helps... Sorry for being longwinded! It's just that there's a LOT of good resources out there, and I've barely scratched the surface. I literally have over 100 books about horse handicapping - horses are my focus - I've never even bet sports.