I would like to get the twitter updates from a user account onto my SharePoint site. Please suggest me how to use that functionality.
Woody Windischman has a good example on his blog, it's based on search but could easily be tweaked to pull user updates.
Depending what you're trying to accomplish, you can also use the Twitter Widget: Twitter Profile Widget
If you look at the code, the following piece of code:
Is what sets the user - You can have your user save his twitter name in a custom list, and simply use a little bit of XSLT within a Data View WebPart to pull it out and output the user within the twitter widget code.
On a related note, for anyone with Server using the User Profiles and Activity Feed, it is possible to create a custom listner that can pull twitter posts into the Activity Feed.
Here is a sample project from MS that outlines the creation of a custom listner: http://archive.msdn.microsoft.com/activityfeedsconsole