In my opinion, the best way to that is to register with one of cryptocurrency marketplaces. Visiting bitcoinwisdom.com you can find Markets tab, where main marketplaces are presented. Just register with one, then top up your account (depending on how much money you want to send to the operator a verification procedure may be required) and when the funds are available for you on the marketplace you can buy LTC.
To send LTC from marketplace to your PC you need a wallet installed. My recommendation is to use Litecoin-qt wallet. You can download it from litecoin.org. When using wallet please remember to have it encrypted.
To send coins from marketplace to the wallet you need a address where you send it. You can generate one with your wallet and then use when sending. That's all.