Why does Git tell me “No such remote ‘origin'” when I try to push to origin?

Two problems:

1 – You never told Git to start tracking any file

You write that you ran

git init
git commit -m "first commit"

and that, at that stage, you got

nothing added to commit but untracked files present (use "git add" to track).

Git is telling you that you never told it to start tracking any files in the first place, and it has nothing to take a snapshot of. Therefore, Git creates no commit. Before attempting to commit, you should tell Git (for instance):

Hey Git, you see that README.md file idly sitting in my working directory, there? Could you put it under version control for me? I’d like it to go in my first commit/snapshot/revision…

For that you need to stage the files of interest, using

git add README.md

before running

git commit -m "some descriptive message"

2 – You haven’t set up the remote repository

You then ran

git remote add origin https://github.com/VijayNew/NewExample.git

After that, your local repository should be able to communicate with the remote repository that resides at the specified URL (https://github.com/VijayNew/NewExample.git)… provided that remote repo actually exists! However, it seems that you never created that remote repo on GitHub in the first place: at the time of writing this answer, if I try to visit the correponding URL, I get

Before attempting to push to that remote repository, you need to make sure that the latter actually exists. So go to GitHub and create the remote repo in question. Then and only then will you be able to successfully push with

git push -u origin master