The best way to begin a new language, especially one so different, like Bengali, is to enroll in classes. A skilled native instructor can introduce you to the basics, such as the sounds of the letters and the grammatical structure. Bengali has sounds that that are very different to English and difficult to pronounce, so it is best to learn them properly from the beginning. Classes are also beneficial because you can practice what you learn, with the other students, in classroom activities and be tested on the material as well.
With some of the basics under your belt, you are ready to start teaching yourself. Remember, there are over 200 million Bengali speakers, so there is no shortage of materials. Check out different websites that offer interactive and printable lessons, tips and shortcuts to learning vocabulary and grammar and printouts to practice writing. Many sites allow you to listen to the sounds of the alphabet, as well as to words and sentences. If you can't find text books and CDs in a store, try ordering them online. "Teach Yourself Bengali" by William Radice, introduces letters, some basic vocabulary, prose and poetry, and includes a CD with the sounds of the alphabet and basic words.
After some classes and independent study, try to meet some native Bengali speakers in your community. Visit a Bengali restaurant, where you can not only try out some of your Bengali, but taste some of the delicious food, which is similar to Indian. Most Bengali speakers live in New York, New Jersey, Massachusetts and California. See if there is a Bengali community center, or Bengali students studying at a local school, in your city. Saying "hello" to a native Bengali speaker may surprise them at first, but they will most likely be interested in speaking with you. Another way to practice is by joining chat rooms or by exchanging emails with a person who speaks Bengali. When speaking with a native speaker, ask them to correct you when you make mistakes, so you don't keep making the same ones.
Bengali language movies and TV shows give you a peek in to the culture behind the language. They also allow you to hear the common words, phrases, accents and intonation used by native speakers. If you are going to speak with native speakers, or visit Bangladesh, movies will improve your Bengali and give you something to talk about. Check out movies like "Kela" and "Antarmahal" by Rituparno Ghosh, the most successful Bengali filmmaker (see Resources). While radio can do this as well, movies and TV allow for subtitles, which makes it easier to make sense of the language. Books, magazines and newspapers are helpful because they allow you to see the grammatical structure, as well as commonly used words. Popular Bangladeshi newspapers, like BD Press and BD National News, are available online (See Resources).