Use single quotation mark ' for strings.

var myString = 'String content';

If you need two or more sets of quotation marks, use ' on the outside, and " on the inside

var searchResult = '<li><a href="Result_URL">Result</a></li>';

Prefix jQuery objects with the dollar sign ($) so they can be distinguished from other objects.

var $header = $('#header');

Instead of using the $ variable directly use a wrapper to inject the jQuery object and only use the dollar sign in the local scope.

// The dollar sign will be used only inside the anonymous function here.
(($) => {
    // The variable $ now refers to jQuery.
})(jQuery);

Add any DOM manipulation code and event handlers inside the document.ready() function to make sure the script does not try to find the elements before the DOM has finished loading. This is recommended by the official jQuery documentation.

// Notice how it's a shorthand for a wrapper for the $ variable (as above) and also a document.ready() at once.
// Use this if you only want to write a quick document.ready().
jQuery(($) => {
    $('.elementClass').on('click', () => { // Click event handler.
        alert('I have been clicked.');
    });
});

Try to avoid adding variables to the global scope. A handy way of exposing globals is to namespace them under jQuery as demonstrated with the following example:

(($) => {
    $.extend(true, {
        myModule: {
            // Such deep nesting is not always necessary, the method could be on this level directly
            myClass: { // More of a "class" than a real class of course
                myMethod() {
                    alert('myMethod called!');
                },
            },
        },
    });

    // You can use the above like this:
    $.myModule.myClass.myMethod();
})(jQuery);

When you want to access resources under a given URL of the current web application (like fetching data from a web API endpoint) never hard-code the URL into yours scripts. URLs can change and may depend on the environment (a trivial example being the usage of ApplicationPath that e.g. could prefix URL's during local development but can be empty in the production environment).

Instead inject such information into your scripts from templates.