Premium and Offline Farming
Premium
Players may purchase 30 days of premium membership by either buying it off of the exchange using zeny in game, or by spending real money in the cash shop, $7.99 USD. This provides quite a zeny boost to that character and has several other perks.
You'll eventually want premium on your best farm character since it really does provide a huge zeny and drop boost. Premium is cheapest during the first day of the month when the price has not risen (very cheap, between 5-10mil) but requires you to bid on it every 30 minutes and hope you win one. Hopefully you'll get a premium if you bid on it next month.
Premium is not something that brand new characters should jump at until you have established farmers! When I say established I mean the character who uses your premium can one shot and kill several mobs at once, be it a ranger or blacksmith with AoE. Offline farming is very convenient but if you're only farming 200-400k a night because you don't one-shot the mobs then you won't make up what you spent on this so don't bother.
Offline Farming
Players who purchase premium with real cash receive an item that grants you the ability to farm offline for 31 days. Unfortunately I have confirmed that you will not get this if you buy premium with zeny off of the exchange, you have to buy it. This sucks for many F2P players who can only farm using their phones through the night or use an emulator.
For those that don't mind paying for this feature, it has been added to the Auto combat menu when you open it. If you check this box it will allow you to specify how long you want to farm so you should always add another 120 minutes to maximize your adjusted combat time to squeeze every drop of zeny out of the game.
Fortunately, using the offline farming item affects your entire account so you can offline farm on all characters with just one purchase.