For example when you Google "stackoverflow" the first result links to http://stackoverflow.com with a description, "A language-independent collaboratively edited question and answer site for programmers."
How is Stack Overflow or any other site working to set that description? I am about to put a website online and would like to get a good description of my site indexed. What steps do I need to take to accomplish this?
One way of achieving this is by using the <meta name="Description"> tag as such:
<head>
<meta name="Description"
content="A language-independent collaboratively edited question and answer site for programmers.">
</head>
On SO, that tag seems to appear only when you are using a user agent related to a crawler.
It's a bit hit and miss as to whether Google displays it but these are set using the 'description' meta tag on each page. If Google doesn't think your entire page is relevant to the search query, it will show a 'snippet' instead. Keep your meta description short and relevant (and non-spammy) and it should show within a day or so of being crawled by Google.
Hope that helps
Google has a help page on the subject of site descriptions.
For your own site, you may also want to add a site map for google and others to use.