In terms of valuing option contracts, it is essentially all about determining the probabilities of future price events. The more likely something is to occur, the more expensive an option would be that profits from that event. For instance, a call value goes up as the stock (underlying) goes up. This is the key to understanding the relative value of options.
Like futures markets, options markets can be traded in both directions (up or down). If a trader thinks that the market will go up, they will buy a Call option, and if they think that the market will go down, they will buy a Put option. There are also options strategies that involve buying both a Call and a Put, and in this case, the trader does not care which direction the market moves.
For example: A steel manufacturer importing coal from Australia currently and in order to reduce the volatility of changes in prices he always hedges the coal purchases on a 3 monthly forward contract where he agrees with the seller on day one of financial quarter to supply coal at defined price irrespective of price movements during quarter. So in this case, the contract is forward/future and buyer has an intention to buy the goods and no intention of making profit from price changes.
Still other traders can make the mistake of thinking that cheaper is better. For options, this isn't necessarily true. The cheaper an option's premium is, the more "out of the money" the option typically is, which can be a riskier investment with less profit potential if it goes wrong. Buying "out of the money" call or put options means you want the underlying security to drastically change in value, which isn't always predictable.
When buying or selling options, the investor or trader has the right to exercise that option at any point up until the expiration date - so simply buying or selling an option doesn't mean you actually have to exercise it at the buy/sell point. Because of this system, options are considered derivative securities - which means their price is derived from something else (in this case, from the value of assets like the market, securities or other underlying instruments). For this reason, options are often considered less risky than stocks (if used correctly).