I know this is not a unix question but I also know that many of you use vim editor every day. So hoping to get some help, here it goes:

How can I change my vim config file so that the indentations while c programming take 4 spaces instead of 8?

I want the change to apply any further uses of vim. Not just the current session.

Thanks in advance!

It looks like:
set shiftwidth=4
does the trick.

Thank you!

What is the vim editor? Another version of vi?

That's right. It's a freely available version of vi. It is close to vi and if you can use vi, you can use vim. But it also has quite a few extensions.