The process of dubbing a movie involves translating the original dialogue into the target language and re-recording it with voice actors. In the case of the Tamil fan-dubbed version of The Hangover, it's likely that a team of enthusiasts worked tirelessly to translate the script, record the voiceovers, and synchronize the audio with the original video.
The existence of a popular fan dub for The Hangover highlights a gap in the official market.