How do I trade at BTC-e? I want to sell 1 LTC via BTC-e. 

How does selling LTC for USD takes place at BTC-e? Most probably I'll firstly deposit 1 LTC in the BTC-e wallet and then go to LTC/USD and then enter 1 LTC under the 'Sell LTC' section and click on 'Sell LTC.' What happens after that?

I want to know because I don't want to waste any bit of my hard earned Litecoins!
When you place an order to sell LTC in btc-e it checks if there is an order to buy LTC at the same rate as you specified. If there is order to buy LTC at the same rate as you specified in your sell order it will fill your sell order up to the amount of the buy order. If the buy order amount is bigger than your sell order your sell order will be filled instantly and you will receive BTC and the buyer will receive your LTC. If there is no buy order at the rate you specified the system will wait for someone to buy LTC at the same rate. You can always cancel these orders before they are completely filled, but remember the 0.20% trading fee is taken when you place an order and not when you complete the order.