Form should preferably contain a ID attribute to identify it unique shape on the page:

<form id="meuFormulario" method="GET" action="http://www.meusite.com/ficheiro.php">
  <!-- ... -->
</form>

If the code for the AJAX call is to be executed by clicking a button of type submit or a link , using the .on() , .click() or the like, we have to avoid the normal behavior of these elements in order to that the page is not submitted to the server and / or updated:

$('#meuBotao').on("click", function(e) {
  e.preventDefault();
  // chamada AJAX aqui
});

or if we are performing the AJAX call directly in the submission of the form, using the method .submit() the concept is the same:

$('#meuFormulario').submit(function(e) {
  e.preventDefault();
  // chamada AJAX aqui
});

The elements in the form, so that they follow a $_GET or $_POST must all contain a name attribute whose same is what will allow them to be identified by the server and thus collect their values:

<input type="text" name="meuNome" value="">

Note that these names are unique identifiers, with some exceptions when the goal is to create an array of results or as in radio where only one value is returned from a set of them.

In the .php file where AJAX will send GET , you can get it as follows:

if (isset($_GET) && is_array($_GET)) {
  $meuNome = $_GET["meuNome"];
}
else {
  echo 'Ups... Preciso receber um GET e o mesmo deverá conter dados!';
}