I came to know that Facebook providing a new look by default to their all new users but I am not seeing such activity on my old account. So what to do here to make changes on old Facebook account?

All those reports of a different look for Facebook are a SCAM.
Simply setup to harvest personal information.

I think you are not aware on new look of FB the side bar is more animated in new Look and seeing more interesting. I was also not sure but make small research and find this link so that you can know about this news and look new and fresh look of Facebook -

http://www.news.com.au/technology/cant-wait-heres-how-to-get-facebooks-new-news-feed/story-e6frfro0-1226594527564

That#s simply an update of the current newsfeed that 's connected to insite chat.
It'll be rolled out to all soon enough..

Just turn on your chat and make sure FB is full screen..

Yes Its not accessible for everyone on this time. Okay lets see when my profile will get in touch with update