Make a link use POST instead of GET

You don't need JavaScript for this. Just wanted to make that clear, since as of the time this answer was posted, all of the answers to this question involve the use of JavaScript in some way or another.

You can do this rather easily with pure HTML and CSS by creating a form with hidden fields containing the data you want to submit, then styling the submit button of the form to look like a link.

For example:

.inline {
  display: inline;
}

.link-button {
  background: none;
  border: none;
  color: blue;
  text-decoration: underline;
  cursor: pointer;
  font-size: 1em;
  font-family: serif;
}
.link-button:focus {
  outline: none;
}
.link-button:active {
  color:red;
}

<a href="some_page">This is a regular link</a>

<form method="post" action="some_page" class="inline">
  <input type="hidden" name="extra_submit_param" value="extra_submit_value">
  <button type="submit" name="submit_param" value="submit_value" class="link-button">
    This is a link that sends a POST request
  </button>
</form>

The exact CSS you use may vary depending on how regular links on your site are styled.

You can use javascript functions. JQuery has a nice post function built in if you decide to use it:

JQuery Post

<script language="javascript"> 

   function DoPost(){
      $.post("WhateverPage.php", { name: "John", time: "2pm" } );  //Your values here..
   }

</script>

<a href="javascript:DoPost()">Click Here</A> 

You create a form with hidden inputs that hold the values to be posted, set the action of the form to the destination url, and the form method to post. Then, when your link is clicked, trigger a JS function that submits the form.

See here, for an example. This example uses pure JavaScript, with no jQuery — you could choose this if you don't want to install anything more than you already have.

<form name="myform" action="handle-data.php" method="post">
  <label for="query">Search:</label>
  <input type="text" name="query" id="query"/>
  <button>Search</button>
</form>

<script>
var button = document.querySelector('form[name="myform"] > button');
button.addEventListener(function() {
  document.querySelector("form[name="myform"]").submit();
});
</script>