You have to be clear on what you mean by "JSON".

Some people use the term JSON incorrectly to refer to a plain old JavaScript object, such as [{a: 1}]. This one happens to be an array. If you want to add a new element to the array, just push it, as in

var arr = [{a: 1}];
arr.push({b: 2});

< [{a: 1}, {b: 2}]

The word JSON may also be used to refer to a string which is encoded in JSON format:

var json = '[{"a": 1}]';

Note the (single) quotation marks indicating that this is a string. If you have such a string that you obtained from somewhere, you need to first parse it into a JavaScript object, using JSON.parse:

var obj = JSON.parse(json);

Now you can manipulate the object any way you want, including push as shown above. If you then want to put it back into a JSON string, then you use JSON.stringify:

var new_json = JSON.stringify(obj.push({b: 2}));
'[{"a": 1}, {"b": 1}]'

JSON is also used as a common way to format data for transmission of data to and from a server, where it can be saved (persisted). This is where ajax comes in. Ajax is used both to obtain data, often in JSON format, from a server, and/or to send data in JSON format up to to the server. If you received a response from an ajax request which is JSON format, you may need to JSON.parse it as described above. Then you can manipulate the object, put it back into JSON format with JSON.stringify, and use another ajax call to send the data to the server for storage or other manipulation.

You use the term "JSON file". Normally, the word "file" is used to refer to a physical file on some device (not a string you are dealing with in your code, or a JavaScript object). The browser has no access to physical files on your machine. It cannot read or write them. Actually, the browser does not even really have the notion of a "file". Thus, you cannot just read or write some JSON file on your local machine. If you are sending JSON to and from a server, then of course, the server might be storing the JSON as a file, but more likely the server would be constructing the JSON based on some ajax request, based on data it retrieves from a database, or decoding the JSON in some ajax request, and then storing the relevant data back into its database.

Do you really have a "JSON file", and if so, where does it exist and where did you get it from? Do you have a JSON-format string, that you need to parse, mainpulate, and turn back into a new JSON-format string? Do you need to get JSON from the server, and modify it and then send it back to the server? Or is your "JSON file" actually just a JavaScript object, that you simply need to manipulate with normal JavaScript logic?

If this JSON file won't become too big over time, you should try:

1. Create a JavaScript object with the table array in it

   var obj = {
      table: []
   };
   

2. Add some data to it, for example:

   obj.table.push({id: 1, square:2});
   

3. Convert it from an object to a string with JSON.stringify

   var json = JSON.stringify(obj);
   

4. Use fs to write the file to disk

   var fs = require('fs');
   fs.writeFile('myjsonfile.json', json, 'utf8', callback);
   

5. If you want to append it, read the JSON file and convert it back to an object

   fs.readFile('myjsonfile.json', 'utf8', function readFileCallback(err, data){
       if (err){
           console.log(err);
       } else {
       obj = JSON.parse(data); //now it an object
       obj.table.push({id: 2, square:3}); //add some data
       json = JSON.stringify(obj); //convert it back to json
       fs.writeFile('myjsonfile.json', json, 'utf8', callback); // write it back 
   }});
   

This will work for data that is up to 100 MB effectively. Over this limit, you should use a database engine.

UPDATE:

Create a function which returns the current date (year+month+day) as a string. Create the file named this string + .json. the fs module has a function which can check for file existence named fs.stat(path, callback). With this, you can check if the file exists. If it exists, use the read function if it's not, use the create function. Use the date string as the path cuz the file will be named as the today date + .json. the callback will contain a stats object which will be null if the file does not exist.