This is a very brief introduction to open source software which I delivered at the recent Wyoming Liberty Fest 2009.
Richard Stallman's Four Freedoms of software:
Think "Free Speech", rather than "Free Beer".
A lot of free software is licensed under the General Public License (GPL), developed by Richard Stallman and the Free Software Foundation. Other licenses exist: the BSD license, Artistic License, and a plethora of others. The Open Source Initiative (OSI) tracks licenses and rates how open they are.
Everyone who has used a computer has used free software. More than 70% of the web servers out there are Apache. Mail is relayed across the Internet with Sendmail, Postfix and other open source MTAs. Firefox and Thunderbird are free replacements for Internet Explorer and Outlook, respectively. Google uses and contributes to free software extensively. I wrote this on OpenOffice.org on top of Ubuntu Linux®.
If you run Microsoft Windows® or a Mac, it's easy to get. There are a lot of free programs for those two operating systems. E.g.:PDF Creator is a "printer" for Windows that produces a PDF file.
For a good compendium of free software for Windows, see the OpenDisc project. As many of the programs on the OpenDisc also run on Linux, it's a good way to get your feet wet and prepare for conversion to Linux. For example, I use OpenOffice.org and GnuCash on Linux; both are on the CD.
For portability across multiple Windows machines, Portable Apps.
If you already run Linux, consult your distro repositories.
Most of these programs will pick up the settings for their Microsoft analogs, e.g. Firefox will import your Internet Explorer settings. OpenOffice.org has excellent import and export filters for Microsoft Office file formats. I've been able to work with clients who had no idea I was using OpenOffice.org.
You will hit some retraining issues. No matter how closely a given program imitates another, it won't be an exact clone. So the time to convert is when you would be upgrading anyway. So, for example, six months before your license for MS Word will expire, install OpenOffice.org, and start learning it. This gives you a phased, staggered upgrade path, so you aren't leaning a whole bunch of new programs all at once.
The best place to get help for an application is usually its home page, or special email lists or IRC channels. Another good resource is the Goodbye Microsoft web page.
Once you are running the open source programs you want, then converting to Linux is much simpler. This is because most of the training cost of moving to a new operating system is really the cost of learning the new applications on that OS. Ubuntu is probably the best place for a Linux newbie to start.