How do I give a header it's own stylesheet?

Specifaclly I just want to change this header by giving it's own, color, font, size, weight.etc

<div id="header">
   <a href="google.com">
   <h1>
       <li><a href="#" class="navLink">EXAMPLE LINK</a></li>
   </h1>
</div>

Solution

Firstly, there are several errors in your HTML, which should be fixed first:

<div id="header">
    <!-- needs a closing </a> tag and some text, as well as a full href -->
    <a href="http://google.com"></a>
    <!-- what is your reason for using an LI element here? -->
    <h1><li><a href="#" class="navLink">EXAMPLE LINK</a></li></h1>
</div>

As far as styling, you can use CSS, like so:

h1 {
    color: red;
    font-size: 5em;
    text-decoration: underline;
}

/* etc. */

Search Google for basic CSS tutorials. Once you've decided which styles you would like to apply, simply save your text document as something like "style.css", and add a LINK element to the header of your HTML file (this will allow you to use it as an external stylesheet.):

<head>
    <link rel="stylesheet" href="style.css" />
</head>

There are other methods for applying styles, such as inline styling, etc., but the above is one of the more typical ways of going about doing it.

Here are some resources to get you started:
w3schools CSS tutorial
CSS-Tricks
How to apply stylesheets