How to create web widgets using HTML,CSS or any JS library

Want to create web widget ?

1. It may contain Carousel.
2. It may use web services to fetch the data

My main problem or I can say issue is that i want to create it as a widget which can be use in any website in the world and it will not collide with any other JS, CSS, and HTML.

User just have to use the JS and JS will create HTML, css and fetch data from web services.

Now I don't have much idea regarding JS lib. Which lib should i use so that my JS will colluide with any other JS which are already present in the page. HOw to localize my JS ?

How to create HTML and CSS with JS ?