Exercising options is not a taxable event in the US. The strike will be the cost basis of the stock that you buy, so the profit when you sell the stock will be
price - strike, and that will be the profit on which you are taxed.
However, it's almost always cheaper to sell the option (which will be taxable) and buy the stock at market price. The option should be worth more than the savings you get by buying the stock at the strike (
spot - strike). You'll pay tax this year on the sale of the option if the option is worth more than it was when it vested, but only on the gain, not the full amount that you get. You should have already been taxed on the vested value of the option through a withholding.
For example, if the options were worth $1 per share when they vested and you received 10 contracts (1,000 shares), you would have been taxed on $1,000 of income. IF they are now worth $1.50 and you sell them, you'll be taxed on $0.50 per share or $500 of income. If they're worth less than when they vested, then you have a loss and can deduct that against other investment gains, or defer them until you do have investment gains.
Note: This applies to US taxes only - it does not include any tax ramification from your home country (if any).