In Korean it is called Baduk (바둑).
The Mandarin pronunciation is roughly "way-chee". To pronounce it correctly, both syllables should be said with a rising tone similar to the change in pitch many English speakers use at the end of a sentence to denote a question. While pronouncing the "ch" in the second syllable, the position of the lips and tongue should be like when pronouncing the letter "t".
In pinyin with tones, it's wéiqí (= wei2 qi2).