I want to create a module that displays nodes of a certain node type. Can this be done, and can anyone point me to a place where I can find how to do this?
First thing you should be looking into is module development in general. Everyone has their own way of researching such things, it could be a book such as "Pro Drupal Development" or a online video series such as http://buildamodule.com/
Are you looking to build the module for Drupal 6 / 7 etc all needs to be taken into consideration too.
To answer your question yes, I would imagine creating a block module to display certain node types be fairly easy. However you might be able to do this with views much easier... Just create a new view, filter by node type and add a block display.
There's currently 12,966 sites using the beta3 release of Views 7 (http://drupal.org/project/usage/views). I'd suggest that you install the module and try to produce what you're describing as I suspect it will work fine. A beta3 release suggests that the module is nearing a production release with no new functionality being added.
Be brave, adopt the new software rather than painting yourself in a corner by writing your own custom code.
This is very easy to do in views.module. Just create a view that filters by your desired node type, then create a 'Block' display type. The block will then show in the block admin page and you'll be able to place it on your site as appropriate.