You would need to add an event listener which listens for the keyup (or keydown) event on the textarea.
Once you have that, you would need to check that the keyCode matches the return key (13).
After that, its a simple case of counting the length of the textarea value and splitting its value via the spaces in order to count the words.
var textarea = document.getElementById('textarea');
textarea.addEventListener('keyup', function (e) {
if (e.keyCode === 13) {
var characters = this.value.length;
var words = this.value.split(' ').length;
document.getElementById('characters').value = characters;
document.getElementById('words').value = words;
}
});
<textarea name="TextArea1" cols="20" rows="2" id="textarea"></textarea><br>
<input name="Text1" type="text" id="characters"/>Characters
<input name="Text1" type="text" id="words" />Words