That is a bit complicate if your theme does not support multi sidebar and custom sidebars.

If it does support them then simply create the sidebar and associate it with the page you want to have the widget appear and then add your code to it. Themes that support this function come with an Admin settings page for the required actions.

There are plugins that create custom sidebars but they can be a hit and miss depending on the theme in use. Here are some you can take a look at and see if they work for your needs...

WordPress › Sidebars « WordPress Plugins
WordPress › Custom sidebars « WordPress Plugins
WordPress › Per Page Sidebar Blocks « WordPress Plugins

The actual list page for more: WordPress › Search for Sidebars « WordPress Plugins

Regards,
Zulf

Look for the Widget Logic plugin: it lets you determine on which page/post to show a widget.

On my Blog, I use a plugin called 'Display widgets'. Does just the job. I'm sure 'Widget Logic' will do just that too!

strategy11.com/display-widgets

I had this same question a few months back. Unfortunately, I realized this couldnt be done. Other than making that one specific page a parent or pattern of another template, you can't. In other works, if your theme does not allow you to change the default page style from a sidebar pages to a full width page, you are out of luck. Though some themes actually do support what you need done.(not many.) Its just a matter of finding the right theme.