Well, I made this once for a Google Chrome plugin and thought to share some of the needed code to do a request to this API with my fellow co-workers. I cut out the crap for the Google Chrome modals I used, so basically this is the POST request that is done to the JIRA API. You can use this from anywhere, just use the Basic Auth thing. (or O–Auth, which is essentially better for open networks)

Well, maybe someone else can use it, in your request use the following structure:

jira = {
    "fields":
    {
        "project":
        {
            "key": "Your-Project-KEY"
        },
        "summary": data["story.name"],
        "description": data["story.notes"],
        "issuetype": { "name": "Sandbox item" }
    }
};

jira = JSON.stringify(jira);

$.ajax({
    type : "POST",
    url : configuration.api_url,
    dataType : "JSON",
    async : false,
    headers: {
        "Authorization": "Basic YeahSomethingInAWrap",
        "Content-Type": "application/json",
        "Accept": "application/json",
        "Cache-Control": "no-cache"
    },
    data : jira,
    success : (function(response) {
        // Alert Success Message
        alert("Received.");
    })
});