Focus Input Box On Load

Just a heads up - you can now do this with HTML5 without JavaScript for browsers that support it:

<input type="text" autofocus>

You probably want to start with this and build onto it with JavaScript to provide a fallback for older browsers.

There are two parts to your question.

1) How to focus an input on page load?

You can just add the autofocus attribute to the input.

<input id="myinputbox" type="text" autofocus>

However, this might not be supported in all browsers, so we can use javascript.

window.onload = function() {
  var input = document.getElementById("myinputbox").focus();
}

2) How to place cursor at the end of the input text?

Here's a non-jQuery solution with some borrowed code from another SO answer.

function placeCursorAtEnd() {
  if (this.setSelectionRange) {
    // Double the length because Opera is inconsistent about 
    // whether a carriage return is one character or two.
    var len = this.value.length * 2;
    this.setSelectionRange(len, len);
  } else {
    // This might work for browsers without setSelectionRange support.
    this.value = this.value;
  }

  if (this.nodeName === "TEXTAREA") {
    // This will scroll a textarea to the bottom if needed
    this.scrollTop = 999999;
  }
};

window.onload = function() {
  var input = document.getElementById("myinputbox");

  if (obj.addEventListener) {
    obj.addEventListener("focus", placeCursorAtEnd, false);
  } else if (obj.attachEvent) {
    obj.attachEvent('onfocus', placeCursorAtEnd);
  }

  input.focus();
}

Here's an example of how I would accomplish this with jQuery.

<input type="text" autofocus>

<script>
$(function() {
  $("[autofocus]").on("focus", function() {
    if (this.setSelectionRange) {
      var len = this.value.length * 2;
      this.setSelectionRange(len, len);
    } else {
      this.value = this.value;
    }
    this.scrollTop = 999999;
  }).focus();
});
</script>