Edit in JSFiddle

// **** ENTER YOUR DETAILS HERE ****

// Enter your API Space Id here e.g. 11164198-3f3f-4993-ab8f-70680c1113b1
var yourAPISpaceId = 'YOUR_API_SPACE_ID';

// Enter your access token here
var yourAccessToken = 'YOUR_ACCESS_TOKEN';

// Enter your mobile number in international format here e.g. for the UK 447123123123
var yourMobileNumber = 'YOUR_MOBILE_NUMBER';

// **** Call the service ****

// Create RESTful URL with API Space Id in it
var comapiUrl = "https://api.comapi.com/apispaces/" + yourAPISpaceId + "/messages";

// Setup request JSON
var myRequest = {
  body: "A test sent via the One API",
  to: {
    phoneNumber: yourMobileNumber
  },
  rules: [
    "sms"
  ]
};

// Update UI
$("#target_url").text(comapiUrl);
$("#input").text(JSON.stringify(myRequest));

// Call Comapi "One" API
jQuery.ajax({
  type: "POST",
  url: comapiUrl,
  data: JSON.stringify(myRequest),
  contentType: "application/json; charset=utf-8",
  dataType: "json",
  beforeSend: function(xhr) {
    xhr.setRequestHeader('Authorization', 'Bearer ' + yourAccessToken);
  },
  success: function(data, status) {
    // Succeeded
    $("#output").text(JSON.stringify(data));
  },
  error: function(request, status) {
    // error handler
    $("#output").text("(" + request.status + ") - " + request.responseText);
  }
});

<div class="container">

  <h1>"One" API basic send</h1>

  <hr/>HTTPS POST to: <b><span id="target_url"></span></b>
  <hr/>
  <h2>
    Input JSON
  </h2>
  <div id="input" style="background-color: white;">
    &nbsp
  </div>
  <hr/>
  <h2>
    Output JSON
  </h2>
  <div id="output" style="background-color: white;">
    &nbsp
  </div>

</div>