This is an example taken from Greek Yogurt theme. You need to include something similar in you theme's header.php file, directed to your custom css file.

<link rel="stylesheet" media="screen" type="text/css" href="<?php echo $this->getStyleSheet('main.css')?>" />

What directory holds that header.php file?

It can depend on which theme you're using, but typically you can find it in your THEMENAME/elements folder

Hmm, looks like for the theme I bought, it's located here:

~/public_html/packages/THEMENAME/elements/THEMENAME/common/header.php

It doesn't seem to recognize my custom css file located here: ~public_html/css/myFile.css

What should be path be in the php line of code you provided above to get to my css file? I tried, ...getStyleSheet('/css/myFile.css')... but no luck.

I made sure to add your line of code as the very last line in the file.

that code assumes the css file is directly in the THEMENAME folder i believe...

but, won't everything get overwritten when the theme updates?

absolutely correct! Once you figure out what works, you want to make the appropriate overrides in the appropriate folders to make sure that does not happen. That was my next message after you, hopefully, told me it was working :)

OK, if I place it in that folder it works. Do I then need to build the same folder hierarchy starting from the root, but without the packages folder? That is, I create this directory:

~/public_html/THEMENAME/elements/THEMENAME/common/

and copy in header.php then edit it to insert the line of php code?