OS X offers multiple input method options to offer support for many world languages and regional input conventions. While this allows the system to be set up to work well for people from different parts of the world, the way OS X manages input methods may confuse a few who make use of multiple input methods.
For example, a standard U.S. keyboard layout will have access to the common characters and symbols used in American English, but this will not work as well for typing in French, where the need for common character accents requires a different input method. Therefore, if you commonly write in both English and French, then you may wish to set up these two input methods on your system and switch between them as is demanded by your work.
The settings for input sources are available in the Language & Text system preferences, where you can check the sources you wish to use, and then set up one of two options for switching between those you have selected. The first is to set up a keyboard shortcut, which oddly on some systems is the same Command-Space shortcut used for Spotlight (though this can be changed in the Keyboard Shortcuts system preferences). The second option is to enable the input menu, where the system will show your selected input methods and allow you to choose from them. The menu will also display the national flag associated with the active input selection.
The default behavior for switching input methods in OS X is to do this systemwide, which will have the change affect all applications and documents; however, you can also set the system to allow different input settings for the various documents you have open. To do this, in the Input Sources system preferences click the option to "Allow a different [input source] for each document."
With this setting enabled, bring the desired document into focus by clicking on its window, and then either use the keyboard shortcut or the input method menu to change the method to use for that document. After doing this, if you switch back and forth from this document to a different one, then the input method should switch as well. While this is convenient, do keep in mind that it is only a temporary setting as long as the document remains open. If you close the document and reopen it, the system will revert to the primary input method and discard any previous method you had selected for the document.
This setup may at times confusing to some people, especially if they wish to change their primary input method. Some people may assume that if they close all applications and then change their input method, that it ought to do so for any applications they subsequently use; however, with the option to apply different input methods to each document this is not the case.
By doing this, all you have done is changed the input method for the Finder (which was the foremost application when you made the change), and when you next open another document the system will revert to its primary input method, requiring you to yet again change the input method. Furthermore, even after making this second change in the newly opened program, if you create any additional documents in this program they likewise will use the primary input method by default.
To change your default input method in OS X and avoid having to make these adjustments for each application and document you open, you first have to be sure the setting to allow a different input source for each document is disabled. To do this, go to the Input Sources system preferences and select the option to "Use the same one in all documents." With this setting in place, go to the input menu and select the desired method you would like to have as your primary input source. After this is done, you can go back to allowing a different input source for each document, and any newly opened documents and applications will now use the desired primary input method, until you manually change it for that document.