After having created a few different podcasts on different Drupal sites for different purposes, using a variety of methods, I can speak with a little authority on which methods are the best, easiest, etc. There is an Audio module, and an iTunes module, which help with more advanced podcasting needs... but most people just want a podcast which will allow visitors to either listen while on the website, or to be able to subscribe to the podcast in iTunes or another media player.
If your needs are relatively simple, it's quite easy to get a podcast up and running on your Drupal website:
Step 1 - Make a Podcast-ready Content Type
In one of your content types, add a filefield that allows the uploading of MP3 and/or M4A files, and create a podcast episode or two. Make sure you set the filefield's display to 'Generic Files' for the RSS display settings (at admin/content/node-type/[your-node-type]/display/rss).
(You can also use something like SWF Tools to display a player for the file for regular ("Basic") node views—so people can play the audio file without having to open your feed in iTunes. Otherwise files will just display as links to the downloadable file).
Step 2 - Make a View with a Page and Feed Display
Now, create a view, and in that view, create a list of all your podcast nodes (nodes that have the MP3/M4A files attached) on a Page display, then create a Feed display that shows a few episodes, and attach that Feed display to the Page display.
Step 3 - Avoid a Hassle by Burning Your Feed
Many would recommend trying to get the feed working properly with iTunes by using the aforementioned iTunes module or some other hackery, but there's a much easier option: FeedBurner. You need to set up an account with FeedBurner. Then use FeedBurner to 'burn' one of your feeds—be sure to check the 'I am a podcaster!' checkbox. Fill out all the relevant details, and then look at what your FeedBurner URL is (mine, for example, is http://feeds.feedburner.com/reviewcast-podcast - this is for the ReviewCast).
Install the FeedBurner module on your Drupal site, and then go to its settings page. Click the 'Burn feed' tab to add your new feed - you'll need to know the path to the Feed display that you configured in your View earlier, and the FeedBurner URL (just use the part that's bolded above).
Step 4 - Profit?
Now, clear all your caches (in case the feed you had in your views was cached already), and you should have a podcast page which not only allows site visitors to play files directly, but also offers iTunes (or other service) subscriptions. You can submit your FeedBurner URL to iTunes' Podcast directory if you'd like to be included.