Susan - as I understand it, all podcasts are MP3 files and it should be possible to manually download them if you know the name of the file and its web address.
You "Subscribe" by linking to a web page which is in XML format. A "Podcast Reader" programme uses the information on the XML page to tell it the name and location of the MP3 files so the reader can automatically download them. If you can find the web address of the XML file you can load it into your browser. In a browser the XML displays as a fancy text file.

Using the web site you have linked to, I have gone into the "Music" category and selected a random page - Page containing "subscribe" link.
Half way down it was a square orange button for the podcast link. Next to it is a box which gives the address the button links you to. In this case you can either highlight and copy the address from the box or you can (with a Windoze PC) Right Mouse Click the button and copy the link shortcut.
Paste the link into your browser address bar and it will take you to the following page ...
FOR EXAMPLE - AN XML PAGE

What this page contains is the instructions your podcast reader uses to find the MP3 files. If you search through the page you will find information such as this:-
http://edit.staroftexasradio.com/sounds/announcement_00006624/AMM_Dec_8.mp3
This is where the MP3 is stored. Copy and paste it into your browser and it will go to that location. What happens next? On some set-ups the MP3 file will download. On others your computer will try to open the file in a "media player" and play it from where it lies. It depends on your system, what programmes you use and how they are set.

Hope that makes sense.
Quack!
GtD.