It is relatively difficult for the native English speaker to learn Vietnamese. Like Chinese, Vietnamese is a tone language. It also borrows much of its vocabulary from Chinese. It was originally written using the Chinese writing system, but today Vietnamese is written using an adapted version of the Latin alphabet. There are not as many published or free resources to learn Vietnamese as there are for other languages, but there are enough options to get you started.
The Seasite main page for Vietnamese language and culture has lots of cultural info - history, music, food etc. There is also a Vietnamese language section which has lots of lessons with audio.
This is a great new resource for learning a variety of Asian languages, including Vietnamese. The initial few dozen lessons are available free in your internet browser. The lessons are introduced somewhat like Rosetta Stone, along with some great extras like downloadable transcriptions and grammar, mp3 audio and a flashcard feature. There is a monthly subscription fee which is very affordable, and a downloadable desktop version if you want it. A very interesting course with great value.
FSI Language Courses
This site has downloadable versions (text files are in pdf format and the audio is mp3) of FSI language courses. Vietnamese Volume 1 is available. It is legal and free. This is probably your best free option to learn Vietnamese. The FSI courses are older and a little out-of-date (a lot in some cases) but they are comprehensive learning courses and you just can't beat the price.
Transparent Language offers a free vocabulary trainer to get started learning Vietnamese. Get your Free BYKI™ Lite download by Transparent Language
This is a beginners course in Vietnamese. The layout is simple and builds slowly. I normally recommend Teach Yourself to first get into a language, but this course seems better suited to the complete beginner. The only drawbacks are that it is a little old and it does not come with any audio. Combine this course with another with audio in order to get a more complete introduction to Vietnamese.
Teach Yourself Vietnamese
My usual recommendation for a beginners course in a language is Teach Yourself (when an equivalent Living Language course isn't available). In this case, Teach Yourself Vietnamese seems to give complete beginners a hard time. It is one of the very few courses that comes with audio, so I feel that I must still include it. Combine this with another course (such as the Beginners Vietnamese above) if you feel you may have trouble learning Vietnamese.
This inexpensive downloadable software program to learn Vietnamese is a great tool to have in your arsenal. Lots of vocabulary and phrases, dialogues, audio from native speakers, games and activities and much more to get you started on your path learning Vietnamese.
Pimsleur Vietnamese Comprehensive
Vietnamese Comprehensive is a new addition to the Pimsleur line. Pimsleurs all-audio format is a great introduction to the language, and with it you'll develop a better accent and conversation ability than with any other published language method. It's a great way to begin to learn Vietnamese. For a more in-depth look at how Pimsleur products work, read my review of Pimsleur, or listen to the first lesson of Pimsleur Vietnamese free below!
Additional Resources to Learn Vietnamese
This site has some interesting supplemental resources for learning Vietnamese. There is reading, listening practice, learning through songs, idioms etc.
This is a forum for Vietnamese learners.
These two sites offer online radio feeds to get some real listening practice.
Radio Free Asia - Vietnamese