If you are not familiar with L try reading the manga or watching the anime (Death Note).
Use aliases as often as possible, L never gives his real name to just anyone. He goes by Ryuuzaki most often in the series.
Your voice should sound tired or bored. To get more of an idea on how L speaks watch the Japanese version of the anime (this can be bought at Wal-Mart and other stores, or watched online).
Never reveal anything more than is necessary. With L, information is on a need-to-know basis. If you must say more, make it something random enough to throw the whoever you're talking to off from what you're actually thinking about. When people around get excited or angry, calmly say something that you know will calm them down, even if you don't really mean it.
Always speak calmly. L only raises his voice in extremely dangerous or frightening situations. Life-and-death situations are normally what triggers this, though extremely shocking news may also be an acceptable situation.