A colleague of mine asked me this recently. I realized that the links that I provided recently are great reference information, but if you are just getting started, it’s overwhelming.
My suggestion is this: Get yourself access to a SharePoint Team Site (i.e. a MOSS or WSS site created with the Team Site template). Then explore all the different kinds of Lists available, familiarize yourself with how Views work, and learn how to use the web part page that is the home page of the team site.
Most people learn best by hands on learning. So you need an environment that you can play with. You could look for a hosting provider that will host a WSS site for free for at least a trial period. Or you can stand up a Virtual Machine (e.g. with Microsoft Virtual PC or Microsoft Virtual Server) and download the Trial edition of MOSS. Except that installing MOSS is not quick, and not intended for SharePoint novices. Therefore, you have two options. You can either download a preconfigured Virtual Hard Drive from http://www.microsoft.com/downloads/details.aspx?FamilyID=67f93dcb-ada8-4db5-a47b-df17e14b2c74&DisplayLang=en (assuming you have already downloaded and installed Virtual Server), or you can get access to a hosted trial at http://office.microsoft.com/en-us/products/HA101687261033.aspx. The hosted trial will require a Citrix plug-in (usually no big deal).
When I tried the online hosted trial, it did give me the following warning:
It then continued without a problem.
If you click on “Overview of Windows SharePoint Services”, you get to an environment where you can play with a site.
I was able to create a subsite and put a page into edit mode. This is clearly the fastest way to get to an environment you can play with. However, I assume that the environment will be destroyed or reset as soon as you close out of it, so if you are doing anything you want to keep, this is not a good solution.