I am wanting to set up REST web services inside of Salesforce that can get, create, and change records for a particular object (leads in this case) whenever it is invoked. I will be invoking these methods from an external website. The POST (create) method I will be using is shown below. I will obviously be adding functionality to the web services themselves. I am only looking to figure out how to actually call them rather than how to write them.

@RestResource(urlMapping='/lead/*')
global class MyWebService {
    @HttpPost
    global static id postLead(string firstName, string lastName, string leadSource, string status) {
        lead newLead = new Lead();
        newLead.FirstName = firstName;
        newLead.LastName = lastName;
        newLead.LeadSource = leadSource;
        newLead.Status = status;
        insert newLead;
        return newLead.id;
}

Then in my javascript (jQuery allowed) code on the external site, I would presumably be creating HttpRequest objects that call these methods; however, I can't seem to get anywhere on this topic. I've tested a plethora of different parameters, but my general code is along the lines of

$.ajax(
    method:"get",
    cache:false,
url:"https://myinstance.lightning.force.com/services/apexrest/lead/leadIdHere",
    success: function(data) {
       alert(data);
    }
);

I know that this is in part because you need to authenticate, but I can'r seem to figure out what the URI for that method would be, not how to retain it. I've tried going through this with JSForce (https://jsforce.github.io) but haven't had any luck there (although I was able to get login authentication working with that.

I am just looking to call a simple REST web service that has been written inside of Salesforce from an external webpage using JavaScript.