My best piece of advice would be to watch and take as many *good* lessons (and clinics) as possible. Ideally take lunge lessons, and ride with an eye on the ground as much as possible, that can be a barnmate giving you feedback (mainly on your position and aids).
While books can be helpful in understanding general concepts, you will only learn to ride while riding : ).
I like the "Gymnasium of the Horse" by Steinbrecht, but that's not an easy read. "The Principles of Riding" by the FN are a nice, condensed version of the basic concepts.
"Reite dein Pferd vorwärts und richte es gerade.” Gustav Steinbrecht
FN is the hoity toity way of saying 'the national organization that governs dressage in a given country'.
Or in other words, the national federation. In our case, the USEF (with the USDF having certain parts of the game, such as instructor certification).
The trend in recent years has been to have only one organization per country running horse sports; the international organization (FEI - international equestrian federation) only wants to deal with one organization per country, the Olympic committee wants that too. So the concept of FN.
The national federation runs competitions from training to fourth level in the USA. Higher level tests, such as PSG-Grand Prix, are run under the FEI rules (a sort of gross simplification but gives you an idea).
Find a GOOD trainer - one that has a history of riding and training in dressage. Not a hunter rider that claims to ride dressage (nothing against hunter riders!). I always try to find a trainer that has actually trained their horses to grand prix. I also watch a few of their lessons to see if i like their style and see if their students improve in their lesson. Lastly, and probably most important, i watch how they ride their client's horses. My biggest piece of advice is to be patient. Dressage is not an instant gratification sport - although the smallest of breakthroughs can make your day. Find someone that can work with you on your position, do lunge work without stirrups, and work on the basics. yes piaffe and passage are beautiful to watch and half-pass is really cool, but don't rush - it has taken people years to just get a good seat much less do the fancy stuff (Spanish Riding School students are on the lunge without stirrups for two to three YEARS before they are given the reins). I can't emphasize enough the importance of a good qualified trainer. Remember, the fact that "anyone can be a trainer" as a German instructor told me one time, anyone can claim to teach dressage when they may not be the least bit qualified. The Practical Dressage Manual is a really good book as mentioned earlier. I would also recommend anything by Jane Kidd - she's a pretty good writer and her books are easy to read - plus her pictures are fabulous.
In my experience the toughest thing a hunter/jumper rider has to re-learn is POSITION, POSITION, POSITION! For so long you've been taught to ride in two point or go forward, and dressage is completely different! It is a very hard thing to retrain and I second, third, fourth the suggestions to find a very good dressage trainer, preferably one who has worked succesfully with hunter/jumper folks.
Best of luck to you and welcome to a great discipline!