Anyone know of a good book to learn Arabic in order to unlock the Moreh Nevuchim and other seforim?
Mossad HaRav Kook has Rambam's own Sefer HaMitzvot with his original Judeo-Arabic and the Hebrew translation, side-by-side ("mekor v'targum.") You could probably pick it up from those parallel texts.
If you are simply looking for a Grammar in Medieval Arabic(which if I am not mistaken would be Classical Arabic), you should try an Islamic bookstore, as that is what the Qu'ran is written in and thus what most Muslims need to learn in order to read it in its original language. Or you could try typing Classical Arabic into Amazon as I just did.
If you are trying to learn Judeo-Arabic that could be a bit trickier. First you have the Hebraisms in the language. Then you have the transliteration system(which is not always so standard), as well as adjustments for local dialect as you come into the Modern Arabic period(which the Rambam wrote during the cross over period).
If you are really committed to learning Arabic and Judeo Arabic, I would say start with Classical Arabic, and then tackle some side by side translations such as Shalom suggested. If your goal is to gain a deeper understanding of the Moreh aside from what is available in translation and commentaries by other Judeo-Arabic speaking Rishonim, understand that it will probably take you several years of serious study to develop the necessary fluency to understand the nuance of the language sufficiently. Hatzlaha.
In addition to all the very good advice in the other answers, there is a book by Joshua Blau in Hebrew called דקדוק הערבית-היהודית של ימי-הביניים, which was published by the Magnes Press of the Hebrew University in 1961 originally, with an enlarged second edition published in 1980. This book is a descriptive, scholarly grammar of Medieval Judeo-Arabic, and includes sections dedicated to spelling and pronunciation, morphology, and syntax. The author notes in the introduction that his grammar does not deal with those features which pertain to Classical Arabic, so it would be prudent for anyone using the book to have a basis of understanding in that language before attempting to tackle this book. Instead, Blau concentrates on how Medieval Judeo-Arabic differs from Classical Arabic. For these reasons, this volume would be most useful for someone who already has a grasp of Classical Arabic and would like to understand more fully texts written in Judeo-Arabic.
Blau also published A Handbook of Early Middle Arabic (2002), which I believe has a chapter dedicated to Judeo-Arabic, as well as The Emergence and Linguistic Background of Judeo-Arabic. I have not seen either of these books, but Joshua Blau is one of the foremost experts on Judeo-Arabic in the world. Here is the link to his page on the Hebrew University's website, which contains some links to interesting and useful material related to this topic: http://www.blau.huji.ac.il/
Also, Yehuda Razabi has published אוצר הלשון הערבית בתפסיר ר' סעדיה גאון with the Bar-Ilan University Press. I cannot say anything more about this book, as I have not seen it yet. However, it would likely be useful for someone delving into this subject. Here is the link: http://www.biupress.co.il/website/index.asp?category=7&id=68
Knowledge of Classical Arabic is sufficient; any specifically Medieval (more exactly: 'Middle Arabic') deviations from the classical in the Rambam's language are very minor. And learning the convention for representing Arabic in Hebrew letters as used in the Guide is a trivial task if you know the Arabic alphabet. You can therefore use primers meant for Classical Arabic to learn the basics and dictionaries of Classical Arabic when working through the text. Arabic dictionaries are organized by root, so you need to figure out a word's root before you can look it up, which can be quite a challenge when the root has weak letters that disappear or change in various conjugations or when letters are prefixed, suffixed, or in-fixed (as often happens in plural forms), i.e., just to look up a word in the dictionary you have to have basic competence in grammar and a 'feel' for the language.
Linguistically, there is another layer on top of Classical Arabic itself: Aristotelian philosophical and scientific terminology (as Shalom noted). These are terms that would not be familiar to most people who read Classical Arabic nowadays: Greek terms for which the original translators of Greek texts into Arabic found or invented Arabic equivalents. The Rambam uses these constantly. This issue will come up, by the way, even if you read the Guide in Hebrew: ibn Tibbon created his own matching vocabulary in Hebrew and it is just as unknown to even well-educated contemporary readers of Hebrew.
Learning any language is an enormous amount of work. You can spend years and years and still be just a beginner. Arabic is a particularly complex and difficult language--it is much more complex than Hebrew, for example. It is hard to get anywhere without people to teach you and without hour after hour of struggle.
I'd recommend the standard texts below:
The reason I recommend these is that, while there are some differences between modern standard Arabic and classical Arabic, these are excellent works on the former, and mastering written Arabic will be more than adequate to prepare you to approach classical texts.
The industry standard book for Classical Arabic is "A Grammar of the Arabic Language" by William Wright. This is a translation of a tutorial originally written in German by Carl Caspari. The edition I have is actually two volumes in two separate books.
I am not an expert in Judeo-Arabic or Jewish Arabic of the middle ages. However, I would speculate that a scholar with a mastery of both Biblical Hebrew and Classical Arabic would be able to navigate through Rambam's writings. Modern Standard Arabic (فصحى) grammar has not changed much from the language of the Qur'an (~600 CE). Since Rambam's Judeo-Arabic fell in between these two times, I would not expect his grammar to be vastly different. As Paquda mentioned above, there may be foreign vocuabulary words which are unfamiliar.