With options markets, as with futures markets, long and short refer to the buying and selling of one or more contracts, but unlike futures markets, they do not refer to the direction of the trade. For example, if a futures trade is entered by buying a contract, the trade is a long trade, and the trader wants the price to go up, but with options, a trade can be entered by buying a Put contract, and is still a long trade, even though the trader wants the price to go down. The following chart may help explain this further:
There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with "optionality" embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
Puts are more or less the mirror image of calls. The put buyer expects the price to go down. Therefore, he pays a premium in the hope that the futures price will drop. If it does, he has two choices: (1) He can close out his long put position at a profit since it will be more valuable; or (2) he can exercise and obtain a profitable short position in the futures contract since the strike price will be higher than the prevailing futures price.
Options are available as either a Call or a Put, depending on whether they give the right to buy, or the right to sell. Call options give the holder the right to buy the underlying commodity, and Put options give the right to sell the underlying commodity. The buying or selling right only takes effect when the option is exercised, which can happen on the expiration date (European options), or at any time up until the expiration date (US options).
The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.