How to integrate WEB form into an existing site?

I hope my question isn't inappropriate:

I am inexperienced and it seems I have no support right now from the Company I work for. I developed some Windows forms which is doing some work on a database, It's working ok but I don't want my users to install the application just to register into a database ( name, phone number, so on and so on, then hit register). I want to create a web form which will do it, and this web form I want to work from a site created by the company, when someone clicks a label on the main site like "Register" I want my web form to open, register then hit register and that's it. Creating the web form doesn't seem hard, the problem is I don't know how to publish it to the site, do I have to ask them to provide me the web server and name ? can I give them a package and they can integrate the form into the web-site?

This is my blocking point. I attach a picture of how I want it to look, but that doesn't matter really, I just want to know how to integrate it to the main site.

Registration example