Ensure that Audacity is installed. While there are other sound editors out there, Audacity is regarded as the industry standard - and it's free and open-source. There's really no excuse not to use it. Get a copy of the most recent Stable Windows, Mac, or Linux version here.
Important: You will also need the LAME mp3 encoder in order to export your podcast in the most compatible format. There is a link to the encoder - as well as instructions on how to install it - here (The file will be inside of a zip archive - to retrieve it, simply double click on the file and drag and drop it to where you want it to go).
Plug in your microphone and headphone set. Ideally, the headphones should cover the ears and be noise cancelling, but any set will do. The podcaster simply needs to be able to monitor their levels as they speak. The microphone should automatically be detected and ready to go; if not, check out the help here, in the section "Configure the microphone as your recording source."
Get Audacity ready for recording. The one default setting you may wish to change is "Software Playthrough," under Audio I/O in Edit -> Preferences. This will allow you to listen to what you say into the microphone as you say it (albiet with a slight delay). If other settings need to be changed, more detailed directions are here, in the section "Preparing to Record".
Throw on the headphones and monitor your voice as you record. Microphone strategy (ie, how far to hold it away from you, where to hold it, etc) will differ depending on what kind of microphone you have.
Have a script prepared (or at least an outline) and take your time...Do as many takes as needed. Some test runs will probably be necessary to get used to editing with Audacity. There is a sample set up on Forever Geek:
Bear in mind that a longer podcast means a bigger file size, and a longer time to download. However, as most people will be streaming the file using broadband, anywhere from 5 to 10 megabytes (roughly 7 to 12 minutes) should be more than acceptable. Those on dial up will be frustrated with anything over 3 megabytes, but dial up users are quick becoming a minority - it's up to the author how to accomodate them.
If you want to save a draft of your project, simply use File -> Save Project As. This will save a .aup file that preserves your project exactly as you see it.
When you're happy with your podcast, click File -> Export as Mp3 to save an mp3. If you haven't already, locate the lame_enc.dll file that you got earlier if Audacity prompts you for it.
Check to make sure that the file size isn't too big (if you're approaching 15 megabytes, you may wish to consider editing it down some or re-recording it).
Upload the file to the web. The easiest way is to store it at Mid Hudson; however, any filehosting service will do.
Once the item is posted, link to the item's entry from a blog post (or anywhere). The link will allow users to stream and/or save the audio file.
The best resources are Google searches and a del.icio.us tag search for "Podcasting." There's a wealth of information on the subject out there.