Depends on what you want to do. There are several plugins. To push build artifacts to update sites. That could range from a simple copy to sftp or to deploying your app to an application server. Almost everything is possible.
In addition there is the promotion plugin, that you can use for automatically or manually promoting builds. You can add actions to promotions like sending out an email or running another job or ...
If you want specific answers, post some more information on your system.
Example questions to answer:
* What options do you have to push something to your update site?
* What language is you app written in (e.g. java, php)? What tool do you use for building (e.g. ant, maven)?
* What does your update site consists of (e.g. WebDAV, Website hosted by apache)
* Does hudson and the update site run on the same box?
* .....