When a volatility skew exists, it can take one or both of two forms – a vertical skew, whereby different striking prices have distinctly different implied volatilities, or a horizontal skew, where different expiration months have vastly different implied volatilities.
The best strategy for taking advantage of the horizontal skew is a calendar spread – buying the long-term options and selling the short-term ones.
For vertical skews, the strategy depends on which way the skew is distorted and if the options are expensive or cheap.
In this chart for SPX, implied volatility tends to decrease monotonically with strike price. Excluding expiration-day effects, SPX exhibits a reverse skew – that is, the lower striking prices have the higher volatilities.
In cases of reverse skews, the best strategies are 1) a call backspread or 2) a put (ratio) spread.