While you may wish to use a library, such as the excellent jQuery, you don't have to: all modern browsers support HTTP very well in their JavaScript implementations via the XMLHttpRequest API, which, despite its name, is not limited to XML representations.
Here's an example of making a synchronous HTTP PUT request in JavaScript:
var url = "http://host/path/to/resource";
var representationOfDesiredState = "The cheese is old and moldy, where is the bathroom?";
var client = new XMLHttpRequest();
client.open("PUT", url, false);
client.setRequestHeader("Content-Type", "text/plain");
client.send(representationOfDesiredState);
if (client.status == 200)
alert("The request succeeded!\n\nThe response representation was:\n\n" + client.responseText)
else
alert("The request did not succeed!\n\nThe response status was: " + client.status + " " + client.statusText + ".");
This example is synchronous because that makes it a little easier, but it's quite easy to make asynchronous requests using this API as well.
There are thousands of pages and articles on the web about learning XmlHttpRequest — they usually use the term AJAX – unfortunately I can't recommend a specific one. You may find this reference handy though.