How to create a "show more" button and specify how many lines of text can be initially shown

Starting from your fiddle and wrapped the content into a <div> with a default class of content, used for selection and a class called hideContent which will be swapped with showContent when clicking the show more/show less link.

I also removed the <p> the text was in. The text is now within the content-div and we are also now able to apply correct height and line-height settings.

HTML:

<div class="text-container">
    <h1>Title goes here</h1>
    <h2>Subtitle</h2>
    <div class="content hideContent">
        Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
        <p>Some more text</p>
        <ul>
            <li>Some more text</li>
            <li>Some more text</li>
            <li>Some more text</li>
        </ul>
    </div>
    <div class="show-more">
        <a href="#">Show more</a>
    </div>
</div>​

CSS:

.hideContent {
    overflow: hidden;
    line-height: 1em;
    height: 2em;
}

.showContent {
    line-height: 1em;
    height: auto;
}

I'm assuming setting the line-height will ensure it is the same in all browsers. I'm not 100% certain on that though.

I attached a click event to the "show more" link which switches the classes on the div using jQueryUI switchClass():

$(".show-more a").on("click", function() {
    var $this = $(this); 
    var $content = $this.parent().prev("div.content");
    var linkText = $this.text().toUpperCase();    

    if(linkText === "SHOW MORE"){
        linkText = "Show less";
        $content.switchClass("hideContent", "showContent", 400);
    } else {
        linkText = "Show more";
        $content.switchClass("showContent", "hideContent", 400);
    };

    $this.text(linkText);
});​

JsFiddle Demo - show more / show less and applying line-height and animation

$(".show-more a").on("click", function() {
  var $this = $(this);
  var $content = $this.parent().prev("div.content");
  var linkText = $this.text().toUpperCase();

  if (linkText === "SHOW MORE") {
    linkText = "Show less";
    $content.switchClass("hideContent", "showContent", 400);
  } else {
    linkText = "Show more";
    $content.switchClass("showContent", "hideContent", 400);
  };

  $this.text(linkText);
});

div.text-container {
  margin: 0 auto;
  width: 75%;
}

.hideContent {
  overflow: hidden;
  line-height: 1em;
  height: 2em;
}

.showContent {
  line-height: 1em;
  height: auto;
}

.showContent {
  height: auto;
}

h1 {
  font-size: 24px;
}

p {
  padding: 10px 0;
}

.show-more {
  padding: 10px 0;
  text-align: center;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.0/jquery.min.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.min.js"></script>

<div class="text-container">
  <h1>Title goes here</h1>
  <h2>Subtitle</h2>
  <div class="content hideContent">
    Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata
    sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.
    <p>Some more text</p>
    <ul>
      <li>Some more text</li>
      <li>Some more text</li>
      <li>Some more text</li>
    </ul>
  </div>
  <div class="show-more">
    <a href="#">Show more</a>
  </div>
</div>

The above code is an example only but should get you started into the right direction.

If you're searching for a css only solution check this out:

HTML

 <div class="show-hide-text">
  <a  id="show-more" class="show-less" href="#show-less">Show less</a>
  <a  id="show-less" class="show-more" href="#show-more">Show more</a>
  <p>
    Lorem Ipsum is simply dummy text of  the printing and typesetting industry...
  </p>
</div>

// CSS

.show-hide-text {
  display: flex;
  flex-wrap: wrap;
}

.show-hide-text a {
  order: 2;
}

.show-hide-text p {
  position: relative;
  overflow: hidden;
  max-height: 60px; // The Height of 3 rows
}

.show-hide-text p {
  display: -webkit-box;
  -webkit-line-clamp: 3; // 3 Rows of text
  -webkit-box-orient: vertical;
}

.show-less {
  display: none;
}

.show-less:target {
  display: block;
}

.show-less:target ~ p {
  display: block;
  max-height: 100%;
}

.show-less:target + a {
  display: none;
}

An example: https://codepen.io/srekoble/pen/WGBzZa?editors=1100