There are many different options for recording or broadcasting your all or a part of your computer screen.  Which one is best for you depends on your needs.  Here are some options, there primary strengths and weaknesses and a short bit about how to use them:

Canvas Conference

This is integrated in to the Canvas LMS, and lets you broadcast your screen, webcam video, and/or audio to members of your class or canvas group.  It does not (yet) let you record the broadcast, and there is no mechanism to let the general public access your broadcast (although you can create a guest account to let someone outside of your class join).  To set up your own Canvas course go to https://canvas.instructure.com.  This tool uses Java.

WebEx Conference

This tool will require you to install a plugin to work.

Jing

Quicktime

Camtasia

ScreenChomp