Renchan has stopped by to explain some of the intricacies of Death Note Kanji, as an introduction for noobs like me. The rest is penned by her.
Kanji has many different pronunciations depending on the Kanji and what it is paired with. In anime, they are allowed to play with this a bit in order to create fictional names. Tsugumi Ohba, the creator of Death Note, was quite careful in this regard, both with the criminals Light killed, and Light himself. He did not want to "hurt anyone's feelings" by using their name.
A lot of different anime do this, actually. There's a well known example from Naruto, the character of Haruno Sakura. While Sakura is a common name, if you put her name together, it translates to "haru no sakura", or "the spring's cherry blossom".
How does this tie into Yagami Light? Well, his name is spelled night god moon. The first Kanji is the sign for "night" or "yoru", the second is God or "kami", and the last one is for "moon" or "tsuki".
It is really just a case of "oooh, look, I can make these sounds by pairing these Kanji together!" Most people would pronounce moon as "tsuki", but the creator chose to say it is pronounced as Light. This follows a trend my sensei says as "kira kira" (ironically this translates to sparkle) names, where you choose random Kanji and say what they mean.
This bit is total guesswork on my part, but having light, dark, and God kind of shows Light's duality as a character.