Realistically, when you say Rest, you would want a service with endpoints, which uses HTTP verbs (GET, POST etc), and does the exact job as it says in the name. If your site is completely in Javascript, then Ajax would be your friend, since it enables you to raise GET, POST XMLHttpRequests. You could also consider using JQuery for future development instead of Javascript. For example, if you wanted to use an API, and make a POST request to one of the API functions, you could do something on the lines of:
req.open("POST", url, true);
req.setRequestHeader("Content-Type",
"application/x-www-form-urlencoded");
req.send(form-encoded request body);
where url is the link to the api function online.
Or, if you had the option, you could develop RESTful services using ASP.NET Web API using C#, and then call/consume them using JavaScript/JQuery
Here is something to get you started:
http://rest.elkstein.org/2008/02/using-rest-in-javascript.html
http://blogs.msdn.com/b/brunoterkaly/archive/2011/11/17/how-to-consume-restful-services-using-jquery-and-or-javascript.aspx
-- addendum
SkyDrive Rest API in essence tells you that the SkyDrive API supports these set of HTTP verbs, and the URI to use those verbs. Now you can raise a request using Javascript, C#, PHP etc, but you will always have to use the same URI provided by the REST API to make the call and get/post the resource. Doing this ensures that every time you use the REST API to do an action (GET, POST), you will always get consistently same results no matter where you call from (C#, Javscript, PHP). If you look at their code examples, all GET requests (C#, Javascript, Objective C) use the same REST URI. ( http://apis.live.net/v5.0/folder.a6b2a7e8f2515e5e.A6B2A7E8F2515E5E!114).
So in essence, you would have something like :
BaseURI: http://apis.live.net/v5.0/ (this will be the BASE uri for any type of request like GET, POST)
Location of Resource: folder.a6b2a7e8f2515e5e.A6B2A7E8F2515E5E!114
Authentication Token: access_token=ACCESS_TOKEN
And then you will have to create an HttpWebRequest if you use C#, and set the RequestType to GET (the verb), and construct the URI from the pieces given above (BaseURI + ResourceLocation + AuthToken), and make sure it matches the format for the GET request in REST API, and execute the request. If you are using JavaScript, you can create XMLHttp Request (AJAX), as they have shown the example. REST API acts as an endpoint, which says, "If you want to use me to GET a resource, this is the URI you will have to call, and you will have to pass all the information specified by the URI"
Have a look here about using SkyDrive REST API in C#
Can't download complete image file from skydrive using REST API
You can also use MS INteractive SDK to get an idea of the difference between JavaScript and REST implementation:
http://isdk.dev.live.com/ISDK.aspx