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Ajax/REST calls do let know when they succeed or fail, that is the whole point.
And you do not need to convert code to synchronous calls.

In the old days you would use Callback functions, nowadays you use Promises
(you can even mix these, Callbacks are executed first)

The best post explaining all this async stuff is:
(it has 2757 upvotes, you can +1)

http://stackoverflow.com/questions/14220321/how-do-i-return-the-response-from-an-asynchronous-call

Code

because Link-only posts are not encouraged and the admins are watching me

orginally from a jQuery answer

Here is code with both Callback functions and Methods chained to the $.ajax Promise
learn to use Chrome Snippets to run SP code without going through a long & complex built proces

    console.clear();
    var site=_spPageContextInfo.webAbsoluteUrl;
    var listName='Documents';
    $.ajax({
        url: site + "/_api/web/lists/getbytitle('" + listName + "')",
        method: "GET",
        contentType: "application/json;odata=verbose",
        async: true, // is the default value, so you can leave it out
        headers: {
            "Accept": "application/json;odata=verbose",
            "X-RequestDigest": $("#__REQUESTDIGEST").val()
        },
        success:function(data){//this is a Callback function
            console.log('success Callback', data)
        },
        error:function(data){//this is a Callback function
            console.log('error Callback', data)
        }
    }).done(function(data){//this is a method on the Promise chain
        console.log('success ',data);
    }).fail(function(data){//this is a method on the Promise chain
        console.error('error ',data);
    }).always(function(data){//this is a method on the Promise chain
        console.log('always ',data);
    });

So the .done method is interchangable with the success Callback

Note that they are both executed in this example.. Callbacks first.

(modern) Promises are more powerful, (oldschool) Callbacks are used in most blogposts.

I had to RTFM as well

.success and .error methods you see in blogposts are deprecated since jQuery 1.8 (use .done and .fail) but do still work

###Yes you can do ajax without jQuery

You do not need that 90KB library, it is just a fancy wrapper around native JavaScript code:

var site=_spPageContextInfo.webAbsoluteUrl,
    listName='Documents',
    xhr = new XMLHttpRequest(); 
xhr.open("GET",site+"/_api/web/lists/getbytitle('"+listName+"')", true);
xhr.setRequestHeader("Accept","application/json;odata=nometadata");
xhr.setRequestHeader("X-RequestDigest",document.getElementById('__REQUESTDIGEST').value);
xhr.onreadystatechange = function (data) {
  if (xhr.readyState != 4) return;//no response received yet 
  if (xhr.status===200) console.info('success');
  console.info('I got:',listName,data);
};
xhr.send();

A modern replacement for XMLHttpRequest is fetch, but it does have some drawbacks: https://davidwalsh.name/fetch
You do need a polyfill becuase only Microsoft Edge 14 now supports it.

Promises are native JavaScript as well but also require a polyfill, Edge is fine but IE still stinks.
Note that jQuery does done and fail, native JS is then and catch

When diving deeper into REST, be sure to understand the different odata responses: https://blogs.office.com/2014/08/13/json-light-support-rest-sharepoint-api-released/

###SharePoint related posts:

• Differing ways to make executeQueryAsync calls - Function.createDelegate (is old IE8 code)
  Explains how to pass data to a succeed function, and why createDelegate is pointless nowadays

iJS