The iTunes directory is a great way to browse, discover, and download podcasts. But, as of now, there is no way to subscribe to the podcast's feed directly from your iDevice. However, as always, there is an app for that.
iCatcher! by Joeisanerd, is a magnificent solution for downloading, streaming, subscribing to, and managing podcasts on iOS. If there is a specific feature that you are looking for in a podcast app, there is a good chance that it is already in iCatcher...