Basics
For people new to asexuality, there are various resources around the internet including FAQs, audio lectures, and 1st person narratives. If you are completely new to asexuality, I have two recommendations.

Asexuality, the Wikipedia article on the subject.

AVEN’s General FAQ

The AVENwiki

Stories

Perhaps the best way to understand asexuality is to understand the stories of people who are asexual.

First Person:  We’re married, we just don’t have sex.  An article from the Guardian.

Story of an asexual couple in their own words. This couple was interviewed about their asexuality for a media article, which claimed to be a first person narrative. They felt it misrepresented them, so they wrote their own version.

I’m not Broken. An avenite wrote a piece for a highschool literature class, posted in AVEN’s library forum.

Asexual Perspectives.  A post by the blogger Ily.

What Planet am I from?
And what would you do with him? Two posts from the blogger Rainbow Amoeba.

Other

Asex 101. A lecture by David Jay, the founder of asexuality.org.

AVENues, the bimonthly newsletter of AVEN is a good source of information on thinking about asexuality as well as asexual news.

Asexual Perspectives. Another good resource on asexuality.org.

Asexuality Aotearoa New Zealand. Information about the asexual community in Aotearoa New Zealand.

Asexual sites. A comprehensive listing of asexual sites around the internet.