No, AMT calculations can be difficult (see the FAQ about the steps). You may need professional help, such as that of an accountant, a tax attorney, or someone experienced in complex tax returns. You should at least acquire tax-planning software or a tax-preparation guidebook.
While we do not recommend that you undertake AMT calculations on your own, you can better understand the process by taking a look at IRS Form 6251 (Alternative Minimum Tax—Individuals), the line-by-line instructions of Form 6251, and IRS Form 8801 (Credit for Prior Year Minimum Tax—Individuals, Estates, and Trusts).
See also a pair of articles on this website that introduce the concepts of the AMT:
You also need to consider state income tax when exercising ISOs and selling the resulting shares. States that impose income tax may have their own form of the AMT (e.g. California; see Schedule P).
IRS Makes Mistakes Too!
Lastly, be aware that (like taxpayers) the IRS sometimes makes mistakes. The US Treasury reported in July 2008 that some IRS examiners have made procedural errors when reviewing AMT returns that the IRS computers flagged for discrepancies (for the calendar year 2006, IRS computers found 226,000 differences between the AMT figures taxpayers reported, or didn't report at all, and the amounts the computers calculated). Some of these mistakes resulted in an incorrect computation of AMT. The Treasury reports that it will focus on AMT procedures in annual training of IRS staff. However, if the IRS reports a discrepancy in your return and produces a different computation of AMT, you may still want your tax advisor to run the numbers again to double-check the IRS result.