If you want to stay on the same page when switching the language (the same content in the new language) you have to have menu item associations activated. Check the option setting for "Menu associations" in the Language Filter Plugin. It must be set to 'Yes'. If it was 'No' and you have already created sets of translations you can associate all the menu items in Joomla! in one go using Synchronizing Associations functionality.

If you want to switch languages at the article (or contact or news feeds) level you have to use the KMFT Language Switcher module if your Joomla! version is lower than 3.1.

The KMFT Language Switcher module also provides some other functionality. For more information please visit Enable Language Switcher Module