I recommend using BTC-E.com for the exchange. There are many others that will work as well.
|By fanquake, jaromil and gavinandresen [see page for license], via Wikimedia Commons|
1. Buy Bitcoins see my previous post
2. Open an account with a bitcoin exchange such as BTC-E.com
3. Fund your exchange account with bitcoins. There should be a link to fund the account with bitcoins. The exchange will give you a bitcoin address to send the funds to. Copy this address and then go to your bitcoin wallet and click "Send Coins". Enter the address given by the exchange. Your coins should transfer in about an hour.
4. Place a bid on litecoins either at the market rate if you want immediate execution or at a lower rate if you want to try to pay less and wait for the sale to go through. Once the trade executes, the litecoins will be deposited to your account.
5. Send the litecoins from the exchange to your wallet (you need to download a litecoin wallet first. You just need the address of your litecoin wallet. Place this in the "Send To" field on the exchange website and the litecoins should be in your wallet in 10 minutes.
This will work for any crypto-currency that you want to purchase. You just need to find an exchange that allows the trading between the two currencies that you are interested in. Here is a list of exchanges with their volume and currencies.