How can I find out the exact expiration date of a patent?

For US patents, it is not as simple as you might think. If the filing date of the application is before  June 8, 1995, it is simply 17 years from the issue date.  However, patents with filing dates after  June 8, 1995, it is 20 years from the filing date, but if the application refers back to one or more earlier filed case, being, e.g., a continuation or a divisional application, then it is 20 years from the filing of the earliest application, but still further, if the patent has been awarded a patent term extension, you have to add that to the expiration date.