How to make button look like a link?

button {
  background: none!important;
  border: none;
  padding: 0!important;
  /*optional*/
  font-family: arial, sans-serif;
  /*input has OS specific font-family*/
  color: #069;
  text-decoration: underline;
  cursor: pointer;
}

<button> your button that looks like a link</button>

If you don't mind using twitter bootstrap I suggest you simply use the link class.

<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.1/css/bootstrap.min.css" integrity="sha384-WskhaSGFgHYWDcbwN70/dfYBj47jz9qbsMId/iRN3ewGhXQFZCSftd1LZCfmhktB" crossorigin="anonymous">
<button type="button" class="btn btn-link">Link</button>

I hope this helps somebody :) Have a nice day!

The code of the accepted answer works for most cases, but to get a button that really behaves like a link you need a bit more code. It is especially tricky to get the styling of focused buttons right on Firefox (Mozilla).

The following CSS ensures that anchors and buttons have the same CSS properties and behave the same on all common browsers:

button {
  align-items: normal;
  background-color: rgba(0,0,0,0);
  border-color: rgb(0, 0, 238);
  border-style: none;
  box-sizing: content-box;
  color: rgb(0, 0, 238); 
  cursor: pointer;
  display: inline;
  font: inherit;
  height: auto;
  padding: 0;
  perspective-origin: 0 0;
  text-align: start;
  text-decoration: underline;
  transform-origin: 0 0;
  width: auto;
  -moz-appearance: none;
  -webkit-logical-height: 1em; /* Chrome ignores auto, so we have to use this hack to set the correct height  */
  -webkit-logical-width: auto; /* Chrome ignores auto, but here for completeness */
}

/* Mozilla uses a pseudo-element to show focus on buttons, */
/* but anchors are highlighted via the focus pseudo-class. */

@supports (-moz-appearance:none) { /* Mozilla-only */
  button::-moz-focus-inner { /* reset any predefined properties */ 
    border: none;
    padding: 0;
  }
  button:focus { /* add outline to focus pseudo-class */
    outline-style: dotted;
    outline-width: 1px;
  }
}

The example above only modifies button elements to improve readability, but it can easily be extended to modify input[type="button"], input[type="submit"] and input[type="reset"] elements as well. You could also use a class, if you want to make only certain buttons look like anchors.

See this JSFiddle for a live-demo.

Please also note that this applies the default anchor-styling to buttons (e.g. blue text-color). So if you want to change the text-color or anything else of anchors & buttons, you should do this after the CSS above.

The original code (see snippet) in this answer was completely different and incomplete.

/* Obsolete code! Please use the code of the updated answer. */

input[type="button"], input[type="button"]:focus, input[type="button"]:active,  
button, button:focus, button:active {
	/* Remove all decorations to look like normal text */
	background: none;
	border: none;
	display: inline;
	font: inherit;
	margin: 0;
	padding: 0;
	outline: none;
	outline-offset: 0;
	/* Additional styles to look like a link */
	color: blue;
	cursor: pointer;
	text-decoration: underline;
}
/* Remove extra space inside buttons in Firefox */
input[type="button"]::-moz-focus-inner,
button::-moz-focus-inner {
    border: none;
    padding: 0;
}