MySqlConnection connection = new MySqlConnection(MyConString);

public class ConnectionFactory
{
    public static MySqlConnection Create()
    {
        string connectionString = ConfigurationManager.AppSettings["..."];
        MySqlConnection conection = new MySqlConnection(Config.ConnectionStr);
        connection.Open();
        return connection;
    }
}

private void button1_click(object sender, EventArg args)
{
    using ( var connection = ConnectionFactory.Create() )
    {
       connection.Execute("...");
    }
}

public static class Config
{
    public static string ConnectionStr = ConfigurationManager.AppSettings["..."];
}

MySqlConnection connection = new MySqlConnection(Config.ConnectionStr);

static void GetConnectionStrings()
{
    var settings = ConfigurationManager.ConnectionStrings;
    if (settings != null) {
        foreach(ConnectionStringSettings cs in settings) {
            Console.WriteLine(cs.Name);
            Console.WriteLine(cs.ProviderName);
            Console.WriteLine(cs.ConnectionString);
        }
    }
}

// Returns null if the name is not found.
static string GetConnectionStringByName(string name)
{
    string returnValue = null;   // Assume failure.
    var settings = ConfigurationManager.ConnectionStrings[name];
    if (settings != null) {
        returnValue = settings.ConnectionString;
    }
    return returnValue;
}