How does green tea burn fat?

It doesn’t. [1]

For credible, science-based information on obesity and weight loss, check out Weighty Matters, Obesity Panacea, and Dr. Sharma’s Obesity Notes.

Reference:

[1] Phung, O., Baker, W., Matthews, L., Lanosa, M., Thorne, A., & Coleman, C. (2009). Effect of green tea catechins with or without caffeine on anthropometric measures: a systematic review and meta-analysis American Journal of Clinical Nutrition, 91 (1), 73-81 DOI: 10.3945/ajcn.2009.28157