The system is flexible which means there are different ways to do this depending on your requirements.
If you just want different languages for a single store with the same products then the easiest way is to create a new view:
System->Manage Stores then “Create store view"->Save store view
Then set the configuration values for this new view:
System->Configuration, select your store view from the scope drop-down list (top left)
Change the general-locale and possibly currency setup values.
It’s also possible to have product names, category names etc specific to the store view. Just go to the manage products or categories and select your store view from the drop-down list (top left) before changing values.