LaTeX Optional Arguments

How do you create a command with optional arguments in LaTeX? Something like:

\newcommand{\sec}[2][]{
    \section*{#1
        \ifsecondargument
            and #2
        \fi}
    }
}

Then, I can call it like

\sec{Hello}
%Output: Hello
\sec{Hello}{Hi}
%Output: Hello and Hi

Example from the guide:

\newcommand{\example}[2][YYY]{Mandatory arg: #2;
                                 Optional arg: #1.}

This defines \example to be a command with two arguments, 
referred to as #1 and #2 in the {<definition>}--nothing new so far. 
But by adding a second optional argument to this \newcommand 
(the [YYY]) the first argument (#1) of the newly defined 
command \example is made optional with its default value being YYY.

Thus the usage of \example is either:

   \example{BBB}
which prints:
Mandatory arg: BBB; Optional arg: YYY.
or:
   \example[XXX]{AAA}
which prints:
Mandatory arg: AAA; Optional arg: XXX.