Khmer is a truly difficult language for Westerners to learn, harder than Mandarin to speak, and harder than anything other than Chinese or Japanese to read. There are several difficulties. First, many of the vowel sounds are unlike anything in a European language and are only subtly different from one another. Second, crucial differences in meaning depend on distinguishing aspirated and unaspirated versions of consonants, something not critical in most European languages. Finally, the writing system is sufficiently complicated that if you try to learn it up front, it will take a long time to get started on even the most basic conversation. To top it off, there is no standard, intuitive system to transcribe Khmer into the Latin alphabet. Every book and dictionary uses its own idiosyncratic transliteration system, and many of them seem to me to bear little relation to how the words actually sound.
If you really love Cambodia, however, and are motivated to learn this monster of a language, there is no better series of books than "Modern Spoken Cambodian," "Cambodian System of Writing and Beginning Reader," "Intermediate Cambodian Reader," and "Literary Cambodian Reader and Glossary," by Franklin Huffman.
"Modern Spoken Cambodian," ignores the writing system and provides progressive, repetitive exercises that let you get typical sentence structures embedded in your brain. Like all transliteration systems, the one used here is not perfect, but with the help of a teacher or a set of tapes you will eventually figure out the relationship between the letters and sounds. It is helpful to do this before learning the writing system because you'll build up vocabulary and confidence with the (simple enough) grammar. Once you start learning to read you'll find it a big help to recognize the words you are trying to puzzle out.
"Cambodian System of Writing and Beginning Reader" is divided in four parts. The first is a technical description of how the writing system works. It is called an "abugida", sort of halfway between an alphabet and a syllabary. All the rules and exceptions are explained thoroughly. If you find it hard to learn just from a list of the rules, the second part consists of graded exercises that gradually introduce all of the written symbols and then give you practice in writing and transcribing them. The third section consists of a series of heavily annotated readings about basic aspects of life in Cambodia. The book ends with a glossary of all Khmer words used in the readings.
"Intermediate Cambodian Reader" consists of a series of annotated, but unedited examples of written Khmer, including Khmer folktales, descriptions of various monuments around Angkor Wat, including a far more interesting and detailed description of some of the famous bas-relief on Angor Wat than you will find in any English guidebook, excerpts from newspapers dating from the late 1960's, and a complete modern novella, "Sophat." Depending on your interests and the sort of vocabulary you need to learn you could pick and choose among the readings. A variety of Khmer fonts are used, a feature which helps get you used to the many different variations on each symbol that you may find in Cambodia. The book ends with a glossary of all words in this book and the previous one.
"Literary Cambodian Reader and Glossary" is for hard-core students of Khmer literary culture and includes progressivly older literature, mostly poetry. The farther back in time you go the more formal, difficult, and Sanskrit/Pali-influenced the language becomes. If you are marrying into a Khmer family and want to chat with your in-laws, or doing business in Cambodia, this book is probably not what you need.
There are other Khmer textbooks out there. "Everyday Khmer" uses the international phonetic alphabet to transcibe the sounds. That's quite accurate, but it takes a while to learn the IPA itself. The book has useful dialogues, but is weak on repetitive grammar drills, which most people need. "Colloquial Cambodian" is not bad; the transliteration is no more inadequate than any other, and it good dialogues and more exercises than "Everyday Khmer." "Cambodian for Beginners," does a good job of teaching you how to write, but does not cover all the rules and exceptions of the writing system in anywhere near the detail of Huffman's book; also it's transliteration system seems only tangentially connected to how the words are really pronounced. The Foreign Service Institute has a text you can download for free; it seems reasonable, but halfway through starts using the Khmer writing system without teaching it. It's transliteration system seems almost identical to Huffman's
If you've read this review all the way to the end you are really, really motivated to learn Khmer. It is not a language for the faint of heart, but once you've learned a fair bit of it it is really fun. You'll probably want to try out several of the books listed here. Of them all, I think the Huffman books are the most complete and will get you farther towards fluency.