Contact the writer's publisher. You might find you can contact a writer through his publishing house, if he produces books.
Contact a reporter through his parent newspaper or magazine. Most newspaper reporters and columnists have emails connected to their byline. You can also email the editor of the section in which the article appeared. Tell the editor the reason for wanting to make contact. Ask for the wrtier's email address or telephone number or ask that yours be passed on to him.
Approach the writer through his agent or representative. Most agents have a website, phone number, or belong to an association such as the Association of Author's Representatives.
Find the author's website. Most well known authors have a website or blog you can visit. Contact the writer through the email address on his website or by other contact methods provide.
Visit the writer's Linkedn page or his profile on a work site like Elance, Helium or Odesk. Professional writers often have profiles and ways to contact them on outsourcing sites. To use this method you will need to know the writer's user profile name.