The fact that it is a tonal language, with six different tones, that not only emphasize certain words, but change their entire meaning, makes it especially difficult for European or American natives. Training your pronunciation capabilities will cost a lot of time and effort.
The best way to get familiar with a foreign language is by exposing oneself to it. Try to pick it up wherever possible. Walk around with open eyes, read newspapers, listen to local radio stations or watch Vietnamese television. You will notice a lot of useful words and expressions. Of course, the most important thing is: talk, talk and talk! Engage yourself in discussions with locals - be it a bartender, shop-owner or taxi-driver. Try to remember new words and look them up later. Keeping a dictionary on hand is always a good idea (just get one on your smartphone). Don’t become frustrated if Vietnamese people don’t understand you at first. They are not used to foreigners speaking their language as, for example, English-speaking persons are.
If you plan to move to Vietnam, it might be a good idea to start learning the language as soon as possible since it will take you awhile. The Vietnamese Teaching Group offers online lessons, or you can also benefit from some free lessons here.
If you are already in the country, you have different options, especially in the cities. There is the Department of Vietnamese Studies and Vietnamese Language at the University in Ho Chi Minh City that offers six levels of courses for all foreigners with a valid visa. Hidden Hanoi offers basic, survival lessons, but it is rather expensive - about $200.
In case you prefer a more unorthodox way of learning, there are privately organised group meetings in some bars. Or, you can learn Vietnamese in exchange for English teaching at the LESH English Center. Another possibility is finding a tandem partner to meet or organise lessons via internet with programs such as Skype. Search in expat forums for interested people - there are plenty of them!