In the US at least, the strike price for options in a private company is set at whatever price the last 409A valuation was. How this is done is a bit technical, and typically something done by a specialized professional accountant type.

At any rate, the younger and riskier a company is, the lower the 409A usually is, and the more legal wiggle room they have to keep it low so common stock option grants are worth more later on.

For public companies it's whatever the stock price is on the date the option grant is made. If it goes up, the options are worth money. In general, for public companies options are vastly more easy to understand and actually cash out.