An application programming interface (API) is a collection of programming instructions and standards which enables the websites to access their features. It is a software-to-software interface which communicate each other without any user knowledge or intervention. For example, with Facebook API, you can integrate Facebook like pages, with Jot forms you can integrate customized contact form, with Disqus comment system, you can integrate comment system in websites. There are many, few of them have been explained.
JotForm is the WYSIWYG form builder with drag and drop interface mainly developed for web masters. If you need a contact form, survey form, reservation form etc, with date time picker and CAPTCHA quickly, you can setup form, customize it and integrate in your website. Below is the example to create a contact form
If you have a Facebook page of your company, you can add like page of that page in your website.
Once you click get code button, it will provide two different pieces of scripts, once piece to embed just under opening <body> tag and another piece to embed to the place where you want Facebook like button to appear. Follow the instruction.