Is there a way to insert the date and time into a MySQL databse by using the action of a button.
Sure, try putting a script like this in the actionPerformed event of your button:
fpmi.db.runUpdateQuery("INSERT INTO MyTable (t_stamp) VALUES (CURRENT_TIMESTAMP)")
Of course, you will have to adjust MyTable and t_stamp for your table and column names.
MySQL has very good reference documentation for its syntax available at http://dev.mysql.com/doc/refman/5.0/en/index.html. Chapters 11 and 12 should be particularly helpful.
Hope this helps,