How do you pass parameters TO a shortcode?

Let’s say you have a form that sends the data in the following way:

<form method="post" name="car-select" action="<?php echo site_url('/my-page/'); ?>">
    <select name="make">
        <option value="benz">Benz</option>
        <option value="bmw">BMW</option>
        <option value="audi">Audi</option>
    </select>
    <input type="submit" value="Find my dream car!"/>
</form>

Now you want to query some posts based on users choice right? This is where $_POST comes in handy:

add_shortcode('my-shortcode','my_shortcode_function');
function my_shortcode_function($atts){
    // Get the ID from shortcode
    $id = $atts['post_id'];
    // Check if the form data has been sent
    if (isset($_POST['make']) && $id){
        $car_manufacturer = $_POST['make'];
        //Now, you have the form's data. Do whatever you want with it
        return $my_shortcode_values;
    }
}

You have to extend this code to fit your needs, such as defining what to do if there is no form data.