Sometimes you might need to change the dates that a contact was enrolled or dis-enrolled from a program.  Doing that is easy.

First, navigate to the contact profile you wish to change enrollment dates for.  In the Program tab,  you will see a list of enrollments.
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On the enrollment you'd like to change, under the "last change" column, there is a little edit icon next to the current enrollment date.
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If you click on that, a calendar will appear, where you can select the new enrollment or dis-enrollment date.  
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Select your date and click on "save changes" and your new dates will be active in the system.