I have a wordpress site installed on domain www.example.com in my root directory.
I want to install another wordpress site on www.example.com/blog.
How to do this?
It should be possible to do the install, but there is a little configuration needed if you missed it:
http://stackoverflow.com/questions/12209600/another-wordpress-installation-in-a-subfolder
But I don't understand why you want to do that. Unless you want two very different websites. If you want the same site more or less, then use a Custom Post Type that you call blog and that's it.
You can follow this tutorial for setting up WordPress in sub-directories using NGINX:
https://www.digitalocean.com/community/questions/how-to-configure-multiple-wordpress-sites-in-subdirectories-in-nginx
If you would like to manage the two sites from one interface, I would suggest setting up WordPress multi-site:
https://www.digitalocean.com/community/tutorials/how-to-set-up-multiple-wordpress-sites-using-multisite
