Okay, this seems fun, you say, how do I get started? That breaks down into a few questions:
How do I start building with LEGO? You need to pick up a LEGO set or some loose bricks. The easiest thing is to just stop by your local toy store. With some looking you might also find LEGO in clearance sales or garage/yard sales. You can also shop on-line. LEGO Shop at Home is the official LEGO site. You can also buy individual LEGO elements from other individuals at Bricklink.
How do I share my creations with others? There are various websites like Flickr that allow you to show photos to others. For LEGO fans, though, the most important site is Brickshelf, which allows you to set up a free account to share pictures of your LEGO creations with others. Another great site is MOCpages, which allows you to create a quick webpage to feature your creations. I would be remiss if I didn't also point out that Blogger.com allows you to set up a blog for free (like this one).
How do I talk to other LEGO fans? In the "Community sites" section on the front page I have links to a large number of LEGO fan community sites. Most of these have forums that allow you to interact with LEGO fans from all over the world. Some, like Lugnet, are general. Others, like Classic-Castle or Brickfilms, focus on specific aspects of the hobby. Still others, like 1000steine.com, focus on specific countries (or at least post in specific languages). Scan through those forums and find the group that's right for you.
Welcome to LEGO. :) I hope that you find this to be a fun hobby, and I also hope that you make some great vignettes that we can feature here.