Hi La Risa:
I'm guessing that your "Add This" button is a Joomla "Module." In other words, it's like a little widget that you install into your site and that can appear on all (or some) pages. (For more information on Joomla Modules, see http://docs.joomla.org/Module .)
Any Joomla Module has a couple primary characteristics, including the module's Position and its menu assignment. The Position refers to where the Module appears within the active Joomla Template's layout. The menu assignment controls on which pages of your site the Module appears. I'm guessing this is what you need to adjust to "turn off" your module on certain pages of your Web site.
To change a Module's menu assignment, first, log into the back end of your Joomla site as an administrator. Then select the Extensions > Menu Manager item in the main navigation menu. You will see a list of Modules for your Web site, including most likely one titled "Add This" or similar.
Click the Module title to go to the Module's edit screen, and scroll down a little, where you will see a "Menu Selection" area. Click the "Select Menu Item(s) from the List" radio button, and then click on individual menu items related to the pages where you want your Module to appear. (Use Control+click to select multiple menu items.) Finally, click the Save or Apply button to save the changes to your Module. You should then see the changes reflected on the front end of your site.
Working with Modules' menu assignments was one of the most confusing things I encountered when I first started working with Joomla, but it actually ends up making sense once you start to work with it.
Of course, I'm just guessing that you're referring to a Joomla Module; you may be doing something else with your site (for example, working with a Plugin). If the above doesn't make sense, or if you have more questions, post them here. Good luck!
