I would recommend the article Manipulating list items in SharePoint Hosted Apps using the REST API, it contains a thorough description with examples how to perform CRUD operations using REST API in SharePoint 2013.
Below is provided a slightly modified version of function for creating list item from the specified article:
function createListItem(siteUrl,listName, itemProperties, success, failure) {
var itemType = getItemTypeForListName(listName);
itemProperties["__metadata"] = { "type": itemType };
$.ajax({
url: siteUrl + "/_api/web/lists/getbytitle('" + listName + "')/items",
type: "POST",
contentType: "application/json;odata=verbose",
data: JSON.stringify(itemProperties),
headers: {
"Accept": "application/json;odata=verbose",
"X-RequestDigest": $("#__REQUESTDIGEST").val()
},
success: function (data) {
success(data.d);
},
error: function (data) {
failure(data);
}
});
}
// Get List Item Type metadata
function getItemTypeForListName(name) {
return "SP.Data." + name.charAt(0).toUpperCase() + name.split(" ").join("").slice(1) + "ListItem";
}
Usage
//specify item properties
var itemProperties = {'Title':'Order task','Description': 'New task'};
//create item
createListItem(_spPageContextInfo.webAbsoluteUrl,'Tasks',itemProperties,
function(entity){
console.log('New task ' + entity.Title + ' has been created');
},
function(error){
console.log(JSON.stringify(error));
}
);