Currently the best way to buy Litecoins is to trade them for Bitcoins on an exchange market. The main Litecoin exchange is Btc-e. You’ll want to first buy your Bitcoins either locally or on a reputable exchange website.
Step-by-step instructions to buying Bitcoins and exchanging them for Litecoins:
This guide only applies to the USA; these services below only work for US residents.
2) Use BitInstant to transfer from MtGox to Btc-e using the MtGox coupon code to Bitcoin address method:
The address to deposit to can be found on the “Add Funds” page on Btc-e after clicking the “Make a deposit” button for BTC.
3) Now you can convert to LTC by selling Bitcoin and buying Litecoin.