Sometimes when I search in Google, appears a website and just below... several links from that website. Sometimes also (I don't know if it's related) I click on a result and the website shows me the page with the search terms highlighted.
How does that work? I mean, which technology or standard do I have to implement in my website in order to archieve those effects?
Thanks
Do you mean sitelinks?
Google's systems analyse the link structure of your site to find shortcuts that will save users time and allow them to quickly find the information they're looking for.
They only show sitelinks for results when they think they'll be useful to the user.
You can read more here http://www.google.com/support/webmasters/bin/answer.py?hl=en&answer=47334
EDIT
To answer your question, all you can do is make sure you have a well formed site with clear navigation which your users can use and find useful. If your site popular then Google will do the rest.