At expiration, she would use her right if the spot price is above the strike price. On the contrary, a put option buyer tries to protect herself against a fall in the asset price. At expiration, she would use her right if the spot price is below the strike price.
To get these advantages, an option buyer has to pay a premium, which is determined at the time she buys the option. The premium is the price of the option. Option prices differ largely depending on the maturity, the moneyness, and the type of the option. In general, long dated options are more expensive due to their larger time value.
Moreover, in a large number of markets, deep out of the money put options, which protect its buyer against a drop in price, are richer than out of the money call options, which protect its buyer against a surge in the asset price. This reflects the fact that people are more willing to pay insurance against catastrophic events.
For a call option buyer, the payoff at expiration is given by max(0, ST − K) − π, where π stands for the premium, ST is the asset price T at expiration, and K is the strike price. For a K put option buyer, the payoff at expiration is gpaymentiven by max(0, K − ST) − π. In both cases, this implies that losses are limited to the payment of the premium while gains are potentially unlimited. See the following figures.