First of all create an account at: https://btc-e.com. Then click on finances -> deposits. You will then be given an address to send your litecoins to.
Copy this address into your litecoin wallet. I use Electrum. There is a 0.001 LTC fee and you will be asked to authenticate the transaction.
Your transaction will then be in the pending status as it is unconfirmed. Because a transaction has been made, it needs to be confirmed by “miners”. You can check your status within your wallet or in the exchange. BTCe requires 6 confirmations. 1 confirmation takes around 2.5 to 3 minutes so expect a ~15 min wait time. Time for a cup of tea.
“Your deposit will be credited in few minutes after 6 confirmations on the Litecoin network.” is contentious depending on your definition of “few minutes”.
Also note that: “Transaction confirmation on the Litecoin network can take from 1 hour and up to 3 days if you send it without fee.”. What this means is that you want to include a fee. This is like a tip to miners for helping to confirm the transaction. A standard fee of 0.001 LTC is added by the Electrum wallet as noted earlier.
For me it took 22 minutes after which it then appeared in my BTCe account.
The final step is to create a sales order on the exchange converting the litecoins to bitcoins.
A confirmation is shown with a 0.2% fee.
The transfer is then completed.