What are the steps of developing any website? What are the additional steps if a website is also responsive or mobile friendly?

1. I think you have to get clear specific goals first for creating the website. What is its purpose?

2.  Its type, dynamic? static? Where does the content come from? will it be updated on a regular basis or not?

3. Does the client have other websites that it will be part of them?

4. Where will it be hosted? Is s/he using a cloud? Does s/he have a data center?

5. What about the design? Does the client have a specific design in mind? does s/he have a brand? Will it be integrated smoothly when converted to code?

6. The target audience? Who are they?

7. What will be the methods used to evaluate and monitor visits to the website?

8. Is s/he ok with using open source or not? because there are risks involved in using open sources. Open Source Risk Engine, Black Duck. Know your code

the additional steps for being responsive or mobile friendly are simple: use Bootstrap, jQuery Mobile and maybe a JavaScript framework such as Aurelia, React JS, or Angular JS

First you must have client design on either paper or psd will do better, then

You should build the interface for it either from scratch using bootstrap or any other framework or you could take any premium template from market.

When your interface is ready, then for responsiveness you need to implement further css to the theme, for that bootstrap just does fine, then test it on different resolutions, then you are good to go. For any server-side functionality use either php or asp.net.