How to make an introduction movie for website?

I want to create an introduction movie for my website, to demonstrate the manual operation on website and simply add some background musics.

Twitter`s new version introduction movie is a good example:
http://youtu.be/0qqDy5BmYKE Which software is used on this movie?

Or any software can create movie like this?

You want to make a screencast. There is a lot of software out there for both the Windows and Mac OS X platforms.

If you just google for "screencast software" you'll have hours of reading ahead of you. In particular, the Wikipedia page, Comparison of Screencasting Software would be a perfect place to start. They list over 30 screencasting applications, telling you where to download (or purchase) them, which platforms they run on, and if they are commercial or proprietary, or open source or not.

The second charts tells you, for each of the 30+ apps, if they can record audio, record the entire desktop, supports OpenGL or DirectX, and if the app supports editing.

The link at Indoition helps you select a screencasting tool based on features, including:

• recording
• editing
• output
• user
• friendliness
• translation
• usability

I personally use Camtasia from Techsmith for all my screencasting needs and it works great. Easy to use and has lots of output formats to choose from.
They also provide a unlimited 30 days trial which I guess would be sufficient for you to come up with a site intro video.

Disclaimer: This comes from my personal experience, I have no relation with Techsmith.

Two recommendations - Screenr or Amberjack Screenr is a free site, so that's a perk and it works really well on major OS versions like Windows or Mac OSX.

Amberjack is a great first visit tour software that is even better than a video in my opinion, or can be coupled with a video.

Also keep in mind that while some of your users want to watch a video, people like me will much prefer to skim the tour or look at a well put together image and text tour. I personally can't stand watching a video when I can gather the information faster in written form.

There are some people on Elance who offer high quality screencast services at amazingly low prices. Consider having it professionally produced.