How To show Twitter Tweets on asp.net c# Website...?

You can create Widget in twitter and then use that widget in your asp.net site for displaying tweets. Widget contains only html and javascript code, so can be easily used in aspx.

see this link from twitter.com
https://dev.twitter.com/docs/embedded-timelines#customization

You'd probably want to take a look at the Twitter API to get implement a twitter feed.

There are several very good .NET libraries for communicating with Twitter.

I've heard good things about Twitterizer (http://twitterizer.net).