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

SJSU has a license to use WebEx, which allows you to share your desktop or just specific application windows with attendees to your meetings.  Meetings are password protected, but anyone with the password can join.  These broadcasts can also be recorded and shared with other WebEx users.  Sharing with a broader community involves downloading the recording and converting it to another format using an avialable conversion tool, then sharing the converted file.  This tool will require you to install a plugin to work.

Jing

For recording and sharing short (<5 minute) screencasts, Jing is a great tool.  It takes care of the recording and sharing of the file for you, giving you a URL that you are free to distribute.  Jing is a free download from Camtasia.  They also sell excellent tools (Camtasia and SnagIt) for recording and sharing longer videos.

QuickTime X

Free for users of Mac OS X, QuickTime X has a built in screen recording tool.   Just select "New Screen Recording" from the "File" menu, then click the red record button.  You'll be prompted to record the whole screen or just a portion of it.  You can then share by email or post on Youtube or Vimeo by accessing the "Share" item in the "File" menu.

Camtasia

Camtasia is a full featured screen capture and video editing application - if you are doing a lot of video editing of your screen captures it might be worth the cost.

ScreenChomp

If you are interested in recording your iPad screen, check out ScreenChomp.  It is an app that will let you draw on a white background or a picture of your choosing and will record and share the audio and video easily.