Here's about the simplest Hello World! tutorial possible for making a component for Joomla! 1.5.
The very simplest component consists of a single directory and a single PHP file.
In the root folder of your Joomla site there is a "components" directory. Inside the components directory, make yourself a new directory named "com_mycomponent". Inside the com_mycomponent directory, make a file named "mycomponent.php". Place the following three lines inside mycomponent.php:
defined( '_JEXEC' ) or die( 'Direct Access to this location is not allowed.' );
echo "Hello World! Welcome to My Component.";
Now in your web browser load your site. To load your new component, append the URL variable option=com_mycomponent, something like this:
You should see the message from your extremely simple component load in your Joomla site!