I suggest that you take a look at the Getting Started guide on developers.
Important things to know when you start using the JS Search UI are:
- How to configure your search endpoint.
- The concept of Coveo component (explained in the getting started guide) Components available.
- How to configure the way your results are being displayed / Result templates.
A thing you could do to help yourself learning, is playing with the samples available in the repository ([repository root]/pages).
If you would like something more specific, feel free to ask other questions.