We have a dedicated forum for Applets. This is a Game Development forum. I will move this thread to the Applet forum for you. In future please post in the proper forum.
It is recommended that you go through these links to get the most out of the Ranch.
What do you mean by "implement"? Does the applet perform HTTP communication for which you'd like cookie support? If so, the Apache Commons HttpClient library can do that. If you meant something else, please provide more information.