First you need to define the CultureInfo, you can either use the system value or define it separately;
CultureInfo currentCulture = Thread.CurrentThread.CurrentUICulture;
CultureInfo currentCulture = new CultureInfo("fr-FR");
The you need a resource manager to get the values from the correct resx file based on the CultureInfo.
Now assume your application is called MyApp and the resx file default is MessageResource
ResourceManager resourceManager = new ResourceManager("MyApp.MessageResource", System.Reflection.Assembly.GetExecutingAssembly());
Then to get the correct value such as a string called "ExitMessage" you use;
resourceManager.GetString("ExitMessage", currentCulture)