After some struggle I did manage to finally embed the Vimeo video into my blog.
Note that the embed script given at the Vimeo video would not work. Just click on the video that you want to embed. For example the link would come as
Now in order to embed this, there is a wordpress plugin, using which you can write this
[ vimeo vimeo.com/6532611 ]
Do not leave a space between [ and vimeo, I have left a space to show the syntax and avoid the video to get embedded here
i.e. the number of the video and you are done. Happy embedding!