What taxes must be paid when you exercise? And when?

That depends on the type of option. With qualified options, there are no taxes due at exercise (unless you are subject to AMT). And if you hold the stock long enough after the exercise (2 years IIRC), the gain - both the discounted purchase price AND the appreciation - become long term capital gains. That tax is due when the stock is sold. With this scenario, you do have to come up with the option price in cash.

With non-qualified options (or if the qualified options are sold too quickly), the discount is considered to be wages, subject to all of the usual wage withholdings - FICA, federal and state income taxes, and local taxes. Those taxes are due immediately.

A common way to handle the cash requirements with either type of option is to sell immediately after the exercise just enough of the shares to cover the cash requirements of both the exercise and the tax withholdings.

So it is quite easy to get the shares without any cash out of pocket at the time of exercise.

--Peter