JS コード:

$(document).on("click", "#somebutton", function() {          // When HTML DOM "click" event is invoked on element with ID "somebutton", execute the following function...
    $.get(yourServletURL, function(responseJson) {           // Execute Ajax GET request on your servlet URL and execute the following function with Ajax response JSON...
        const $table = $("<table>").appendTo($("#somediv")); // Create HTML <table> element and append it to HTML DOM element with ID "somediv".
        $.each(responseJson, function(index, product) {      // Iterate over the JSON array.
            $("<tr>").appendTo($table)                       // Create HTML <tr> element, set its text content with currently iterated item and append it to the <table>.
                .append($("<td>").text(product.id))          // Create HTML <td> element, set its text content with id of currently iterated product and append it to the <tr>.
                .append($("<td>").text(product.name))        // Create HTML <td> element, set its text content with name of currently iterated product and append it to the <tr>.
                .append($("<td>").text(product.price));      // Create HTML <td> element, set its text content with price of currently iterated product and append it to the <tr>.
        });
    });
});

@Override
protected void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
    List<Product> products = someProductService.list();

    request.setAttribute("products", products);
    request.getRequestDispatcher("/WEB-INF/xml/products.jsp").forward(request, response);
}

<?xml version="1.0" encoding="UTF-8"?>
<%@page contentType="application/xml" pageEncoding="UTF-8"%>
<%@taglib prefix="c" uri="jakarta.tags.core" %>
<%@taglib prefix="fmt" uri="jakarta.tags.fmt" %>
<data>
    <table>
        <c:forEach items="${products}" var="product">
            <tr>
                <td>${product.id}</td>
                <td><c:out value="${product.name}" /></td>
                <td><fmt:formatNumber value="${product.price}" type="currency" currencyCode="USD" /></td>
            </tr>
        </c:forEach>
    </table>
</data>

$(document).on("click", "#somebutton", function() {             // When HTML DOM "click" event is invoked on element with ID "somebutton", execute the following function...
    $.get(yourServletURL, function(responseXml) {               // Execute Ajax GET request on your servlet URL and execute the following function with Ajax response XML...
        $("#somediv").html($(responseXml).find("data").html()); // Parse XML, find <data> element and append its HTML to HTML DOM element with ID "somediv".
    });
});

<form id="someform" action="${pageContext.request.contextPath}/yourServletURL" method="post">
    <input type="text" name="foo" />
    <input type="text" name="bar" />
    <input type="text" name="baz" />
    <input type="submit" name="submit" value="Submit" />
</form>

$(document).on("submit", "#someform", function(event) {
    const $form = $(this);

    $.post($form.attr("action"), $form.serialize(), function(response) {
        // ...
    });

    event.preventDefault(); // Important! Prevents submitting the form.
});

@Override
protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
    String foo = request.getParameter("foo");
    String bar = request.getParameter("bar");
    String baz = request.getParameter("baz");

    boolean ajax = "XMLHttpRequest".equals(request.getHeader("X-Requested-With"));

    // ...

    if (ajax) {
        // Handle Ajax (JSON or XML) response.
    } else {
        // Handle regular (JSP) response.
    }
}

const params = {
    foo: "fooValue",
    bar: "barValue",
    baz: "bazValue"
};

$.post(yourServletURL, $.param(params), function(response) {
    // ...
});

$.ajax({
    type: "POST",
    url: yourServletURL,
    data: $.param(params),
    success: function(response) {
        // ...
    }
});

const data = {
    foo: "fooValue",
    bar: "barValue",
    baz: "bazValue"
};

$.ajax({
    type: "POST",
    url: yourServletURL,
    contentType: "application/json", // NOT dataType!
    data: JSON.stringify(data),
    success: function(response) {
        // ...
    }
});

JsonObject data = new Gson().fromJson(request.getReader(), JsonObject.class);
String foo = data.get("foo").getAsString();
String bar = data.get("bar").getAsString();
String baz = data.get("baz").getAsString();
// ...

document.open();
document.write(responseText);
document.close();

String redirectURL = "http://example.com";

Map<String, String> data = new HashMap<>();
data.put("redirect", redirectURL);
String json = new Gson().toJson(data);

response.setContentType("application/json");
response.setCharacterEncoding("UTF-8");
response.getWriter().write(json);

function(responseJson) {
    if (responseJson.redirect) {
        window.location = responseJson.redirect;
        return;
    }

    // ...
}