if you just want the status updates of one user, you could periodically poll and parse the RSS feed for that user, or alternately twitter has a simple way to get a user’s current status in an easy-to-parse format.
Links to RSS feeds are on the bottom right of a user’s page, although those links seem to have disappeared in the new twitter design. The URL for just the current status is: http://api.twitter.com/1/users/show/username.xml
the other, far more complicated, but ‘nicer’ way would be to use the twitter streaming api. this would push status updates to you in as they are published.