using (SshClient client = new SshClient(sshConnectionInfo))
{
    client.Connect();

    //strCmd is:
    //  mysqldump -h "<server>.dreamhosters.com" -u "<dbuser>" -p"<actual_password>" "<dbid>" > "/home/<user_name>/<temp_file_name>.sql"
    //
    //  with <...> parts are obviously filled in with correct credentials
    SshCommand resCmd = client.RunCommand(strCmd);

    //Check result
    string strExpDesc = resCmd.Error;
    if (string.IsNullOrWhiteSpace(strExpDesc))
    {
        Console.WriteLine("Exported OK");
    }
    else
    {
        Console.WriteLine("Error: " + strExpDesc);
    }
}