Free Open Source Software:
Audacity one of open source's most famous and popular free software. Very powerful and easy to use. Don't forget about screencasts. To learn this software just type in "How to audacity" into Youtube and you have a bunch of great free tutorials to quickly learn the tool.
I have been looking for a web service similar to youtube for audio as an easy way to upload, link, embed, and share. Houndbite appears to be a very simple way for beginner to tryout podcasting.
Create Find and Share Podcasts. You upload and they take care of the rest, the hosting, iTunes subscription. These types of services give you a decent size to start up but once you start building up the space there are premium upgrades.
Web App + Cell Phone:
No equipment needed. Simple and Fast.
Gcast is an incrediblly easy way to start up a free podcast.
1) Sign up for an account
2) Call toll-free anytime at 1-888-65-GCAST (888-654-2278) If outside USA: +1-305-437-8719
3) Type in primary phone number
4) Enter 4 digit pin
5) Record your message, and either:
6) Save and Publish
7) Link or Embed your podcast and player
See Our 5th Grade Podcast for an example.