In the below examples I have used the 'ABC Mappings' as my SharePoint list. The CRUD operations are done against the items in this list.
Create
var payload = '';
var itemCreated = '';
        payload = { SourceField: item.SourceField, SheetName: item.SheetName, CellCoordinate: item.CellCoordinate, DataType: item.DataType, __metadata: { type: 'SP.Data.ABCMappingsListItem' } };
        var siteUrl = window.location.protocol + "//" + window.location.host + _spPageContextInfo.webServerRelativeUrl;
        $http({
            method: 'POST',
            url: siteUrl + "/_api/web/lists/getByTitle('ABC Mappings')/items",
            data: payload,
            async: false,
            headers: {
                "Accept": "application/json;odata=verbose",
                "Content-Type": "application/json;odata=verbose",
                "X-RequestDigest": $("#__REQUESTDIGEST").val()
            }
        }).success(function (data, status, headers, config) {
            itemCreated = data.d.ID;
        }).error(function (data, status, headers, config) {
            alert('error');
        });
Read
var siteUrl = window.location.protocol + "//" + window.location.host + _spPageContextInfo.webServerRelativeUrl;
        $http({
            method: 'GET',
            url: siteUrl + "/_api/web/lists/getByTitle('ABC Mappings')/items?$select=ID,SourceField,SheetName,CellCoordinate,DataType",
            headers: { "Accept": "application/json;odata=verbose" }
        }).success(function (data, status, headers, config) {
            $scope.items = data.d.results;
        }).error(function (data, status, headers, config) {
            alert('error');
        });
Update
Initially you need to find the list item type. For this we can use the below REST call
http://<weburl>/_api/lists/getbytitle('Document Library Name')?$select=ListItemEntityTypeFullName
The function call:
        //Variables
        var payload = '';
        var itemUpdated = '';
        var itemId = item.ID;
        //Create item
        payload = { SourceField: item.SourceField, SheetName: item.SheetName, CellCoordinate: item.CellCoordinate, DataType: item.DataType, __metadata: { type: 'SP.Data.ABCMappingsListItem' } };
        var siteUrl = window.location.protocol + "//" + window.location.host + _spPageContextInfo.webServerRelativeUrl;
        $http({
            method: 'POST',
            url: siteUrl + "/_api/web/lists/getByTitle('ABC Mappings')/items(" + itemId + ")",
            data: payload,
            async: false,
            headers: {
                "Accept": "application/json;odata=verbose",
                "Content-Type": "application/json;odata=verbose",
                "IF-MATCH": "*",
                "X-HTTP-Method": "MERGE",
                "X-RequestDigest": $("#__REQUESTDIGEST").val()
            }
        }).success(function (data, status, headers, config) {
        }).error(function (data, status, headers, config) {
            alert('error');
        });
Delete
 var siteUrl = window.location.protocol + "//" + window.location.host + _spPageContextInfo.webServerRelativeUrl;
        $http({
            method: 'POST',
            url: siteUrl + "/_api/web/lists/getByTitle('ABC Mappings')/items(" + itemId + ")",
            async: false,
            headers: {
                "Accept": "application/json;odata=verbose",
                "Content-Type": "application/json;odata=verbose",
                "IF-MATCH": "*",
                "X-HTTP-Method": "DELETE",
                "X-RequestDigest": $("#__REQUESTDIGEST").val()
            }
        }).success(function (data, status, headers, config) {
        }).error(function (data, status, headers, config) {
            alert('error deleting');
        });