In jQuery, the following would work:

$("#id_of_textbox").keyup(function(event) {
    if (event.keyCode === 13) {
        $("#id_of_button").click();
    }
});



$("#pw").keyup(function(event) {
    if (event.keyCode === 13) {
        $("#myButton").click();
    }
});

$("#myButton").click(function() {
  alert("Button code executed.");
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

Username:<input id="username" type="text"><br>
Password:&nbsp;<input id="pw" type="password"><br>
<button id="myButton">Submit</button>

Or in plain JavaScript, the following would work:

document.getElementById("id_of_textbox")
    .addEventListener("keyup", function(event) {
    event.preventDefault();
    if (event.keyCode === 13) {
        document.getElementById("id_of_button").click();
    }
});



document.getElementById("pw")
    .addEventListener("keyup", function(event) {
    event.preventDefault();
    if (event.keyCode === 13) {
        document.getElementById("myButton").click();
    }
});

function buttonCode()
{
  alert("Button code executed.");
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

Username:<input id="username" type="text"><br>
Password:&nbsp;<input id="pw" type="password"><br>
<button id="myButton" onclick="buttonCode()">Submit</button>