ISOs affect your AMT liability in two ways.

First: The ISO exercise spread increases AMT income for the year of exercise if you hold the acquired shares through that calendar year. The exercise spread is a positive adjustment in your AMT income calculation. (See Line 14, IRS Form 6251, Alternative Minimum Tax—Individuals.) So whenever you intend to exercise ISOs, you should carefully explore the AMT consequences and calculate your potential alternative minimum tax.
Second: Selling ISO shares decreases your AMT income for the year of sale and probably reduces your AMT liability below your regular tax. (See the FAQ on the consequences when you sell ISO shares that generated AMT.) As a result, at sale the AMT credit provides an opportunity to recapture all or a part of any AMT that you paid during the year of exercise.

If you exercise ISOs and sell the shares in the same tax year, you will not have AMT income from the ISOs. You may, however, still owe the AMT as a result of other AMT adjustments or preferences for that tax year. For strategies to minimize AMT, see a related FAQ.