How to capture Enter key press?

Use onkeypress . Check if the pressed key is enter (keyCode = 13). if yes, call the searching() function.

HTML

<input name="keywords" type="text" id="keywords" size="50"  onkeypress="handleKeyPress(event)">

JAVASCRIPT

function handleKeyPress(e){
 var key=e.keyCode || e.which;
  if (key==13){
     searching();
  }
}

Here is a snippet showing it in action:

document.getElementById("msg1").innerHTML = "Default";
function handle(e){
 document.getElementById("msg1").innerHTML = "Trigger";
 var key=e.keyCode || e.which;
  if (key==13){
     document.getElementById("msg1").innerHTML = "HELLO!";
  }
}

<input type="text" name="box22" value="please" onkeypress="handle(event)"/>
<div id="msg1"></div>

Form approach

As scoota269 says, you should use onSubmit instead, cause pressing enter on a textbox will most likey trigger a form submit (if inside a form)

<form action="#" onsubmit="handle">
    <input type="text" name="txt" />
</form>

<script>
    function handle(e){
        e.preventDefault(); // Otherwise the form will be submitted

        alert("FORM WAS SUBMITTED");
    }
</script>

Textbox approach

If you want to have an event on the input-field then you need to make sure your handle() will return false, otherwise the form will get submitted.

<form action="#">
    <input type="text" name="txt" onkeypress="handle(event)" />
</form>

<script>
    function handle(e){
        if(e.keyCode === 13){
            e.preventDefault(); // Ensure it is only this code that runs

            alert("Enter was pressed was presses");
        }
    }
</script>