This is a very common question, I'll post links to other answers below.
A minimal sample: https://jsfiddle.net/aq9Laaew/284188
html:
<html>
<head>
    <meta charset="utf-8">
    <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" integrity="sha384-Gn5384xqQ1aoWXA+058RXPxPg6fy4IWvTNh0E263XmFcJlSAwiGgFAW/dAiS6JXm" crossorigin="anonymous">
</head>
<body>
    <script src="https://code.jquery.com/jquery-3.2.1.slim.min.js" integrity="sha384-KJ3o2DKtIkvYIK3UENzmM7KCkRr/rE9/Qpg6aAZGJwFDMVNA/GpGFF93hXpG5KkN" crossorigin="anonymous"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.12.9/umd/popper.min.js" integrity="sha384-ApNbgh9B+Y1QKtv3Rn7W3mgPxhU9K/ScQsAP7hUibX39j7fakFPskvXusvfa0b4Q" crossorigin="anonymous"></script>
    <script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/js/bootstrap.min.js" integrity="sha384-JZR6Spejh4U02d8jOt6vLEHfe/JQGiRRSQQxSfFWpi1MquVdAyjUar5+76PVCmYl" crossorigin="anonymous"></script>
    <script src="main.js"></script>
    <div class="carousel slide" data-ride="carousel">
        <div class="carousel-inner">
          <div class="carousel-item active">
            <center><p> First slide</p></center>
          </div>
          <div class="carousel-item">
            <center><p> Second slide</p></center>
          </div>
        </div>
        <a class="carousel-control-prev" href="#carouselExampleControls" role="button" data-slide="prev">
          <span class="carousel-control-prev-icon" aria-hidden="true"></span>
          <span class="sr-only">Previous</span>
        </a>
        <a class="carousel-control-next" href="#carouselExampleControls" role="button" data-slide="next">
          <span class="carousel-control-next-icon" aria-hidden="true"></span>
          <span class="sr-only">Next</span>
        </a>
      </div>
</body>
</html>
js:
$(function(){
    $('.carousel').carousel()
})
This creates a bootstrap carousel, the animation works, the carousel automatically switches between first and second slide. But the controls don't do anything.
Here are similar SO posts:
- Bootstrap Carousel Not Responding the problem was a broken link to jquery
 - Bootstrap Carousel controls not working not properly calling carousel()
 - Bootstrap 4 Carousel controls not working popper.js is not properly included
 - bootstrap carousel controls is not working jquery not included
 
I think that my setup is correct, I basically just pasted the carousel sample code into the bootstrap starter template.