The built in language choice page rests at index.php?a=21 like so:

http://www.example.com/index.php?a=21

You will see the language choice form allowing the client to choose the language they wish to see the site in. When the client comes to this page their currently chosen language will NOT be automatically selected in the language choice dropdown displayed on that page.

You can also create links that will change the language for you instead of pushing the client through the language choice form. These can be placed directly in your html design. Find the id of the language you wish to change to within the language admin tool. The default language that comes with your installation is "1" and cannot be removed from the site. All other languages added after that obtain their own id. For example to change to language id 3 you can use a link like that below.

http://www.example.com/index.php?set_language_cookie=3
 
or 
 
index.php?set_language_cookie=3

Change the "3" to the language id of the language you wish to change to and you should be able to use this as a "language" link within your templates (enterprise only) or html to change the language the site is displayed in with one click.