<div>
  <blockquote cite="https://www.huxley.net/bnw/four.html">
    <p>Words can be like X-rays, if you use them properly—they’ll go through anything. You read and you’re pierced.</p>
  </blockquote>
  <p>—Aldous Huxley, <cite>Brave New World</cite></p>
</div>

div:has(> blockquote) {
  background-color: #ededed;
  margin: 10px auto;
  padding: 15px;
  border-radius: 5px;
}

blockquote p::before {
  content: '\201C';
}

blockquote p::after {
  content: '\201D';
}

blockquote + p {
  text-align: right;
}