How to add button inside input

.flexContainer {
    display: flex;
}

.inputField {
    flex: 1;
}

<div class="flexContainer">
    <input type="password" class="inputField">
    <button type="submit"><img src="arrow.png" alt="Arrow Icon"></button>
</div>

Use a Flexbox, and put the border on the form.

The best way to do this now (2019) is with a flexbox.

• Put the border on the containing element (in this case I've used the form, but you could use a div).
• Use a flexbox layout to arrange the input and the button side by side. Allow the input to stretch to take up all available space.
• Now hide the input by removing its border.

Run the snippet below to see what you get.

form {
  /* This bit sets up the horizontal layout */
  display:flex;
  flex-direction:row;
  
  /* This bit draws the box around it */
  border:1px solid grey;

  /* I've used padding so you can see the edges of the elements. */
  padding:2px;
}

input {
  /* Tell the input to use all the available space */
  flex-grow:2;
  /* And hide the input's outline, so the form looks like the outline */
  border:none;
}

input:focus {
  /* removing the input focus blue box. Put this on the form if you like. */
  outline: none;
}

button {
  /* Just a little styling to make it pretty */
  border:1px solid blue;
  background:blue;
  color:white;
}

<form>
  <input />
  <button>Go</button>
</form>

Why this is good

• It will stretch to any width.
• The button will always be just as big as it needs to be. It won't stretch if the screen is wide, or shrink if the screen is narrow.
• The input text will not go behind the button.

Caveats and Browser Support

There's limited Flexbox support in IE9, so the button will not be on the right of the form. IE9 has not been supported by Microsoft for some years now, so I'm personally quite comfortable with this.

I've used minimal styling here. I've left in the padding to show the edges of things. You can obviously make this look however you want it to look with rounded corners, drop shadows, etc..

The button isn't inside the input. Here:

input[type="text"] {
    width: 200px;
    height: 20px;
    padding-right: 50px;
}

input[type="submit"] {
    margin-left: -50px;
    height: 20px;
    width: 50px;
}

Example: http://jsfiddle.net/s5GVh/