If you want to use the official app, just head to http://www.facebook.com/twitter and follow the instructions. There were already a few 'work-arounds', but this is the first offical one.
The why is harder to answer then the how. Some see this as a victory of sorts for Twitter. I see it as a continuation of Facebook's attacks on the site (past recent attacks listed below). You start with the logic that some Facebook users have amassed a large enough following on witter that they do not want to abandon the site. That meant splitting your time between the two sites. With this official app, you can spend more of your time on Facebook confident that your Twitter followers will stay updated. As your followers see a growing percentage of your Tweets coming from Facebook, they jump to the source and become a fan of your page leaving Twitter. Even if Twitter users never 'jump ship', there really is no downside for Facebook.
"Many people have asked us to make Facebook and Twitter work better together for those times when they want to share their content as widely as possible. We agree. Over the next few days, we will be releasing a feature that allows administrators of Facebook Pages to publish their Facebook updates to their Twitter accounts automatically. This will only link Facebook Pages to Twitter, not your individual profile.
If you manage a Facebook Page, you now will be able to decide whether to share updates with their Twitter followers, and you also will be able to control what type of updates to share: status updates, links, photos, notes, events or all of them. If you have multiple Pages, you will have the option to link each of those Pages to different Twitter accounts. This new feature will soon be available at http://www.facebook.com/twitter."
Past recent attacks on Twitter by Facebook:
Berman Post: Facebook Buys FriendFeed
Berman Post: Facebook Getting a 'Twitter Like' Search
Berman Post: Facebook Lite