[boyter]

+1 For the recommendation of Chinesepod. Dimsum http://www.mandarintools.com/dimsum.html is pretty good for translation and the like. The other thing to do is install QQ and talk to Chinese students and the like.

Honestly though, the cheapest way would be get a job in China, get yourself a Chinese girlfriend/boyfriend and don't hang out with expats. Pick somewhere other then Shanghai or Beijing, (Haerbin is a good choice) and immerse yourself in the culture. Also you need to accept you wont be fluent unless you do this for 5 years+

Why cheapest? Well its pretty cheap to live in China. You spend more money in any western country living then you would in a smaller city in China, and you can dedicate yourself to learning the language.