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1. First, create your GTK4 application window and add an Entry field to it using the gtk::Entry::new() method.

2. Create a button widget using the gtk::Button::newwithlabel() method, and set the label to be the desired character that you want to add to the Entry field.

3. Connect a signal handler to the button widget using the connect_clicked() method, which will execute a callback function when the button is clicked.

4. In the callback function, use the gtk::Editable trait's insert_text() method on the Entry field to insert the desired character at the current cursor position.

Here's an example code snippet that adds a comma character to an Entry field when a button is clicked:

use gtk::prelude::*;
use gtk::{Application, ApplicationWindow, Button, Entry};

fn main() {
    let app = Application::new(None, Default::default()).unwrap();

    app.connect_activate(|app| {
        let window = ApplicationWindow::new(app);
        window.set_title("Add Character Example");

        let entry = Entry::new();
        window.set_child(Some(&entry));

        let comma_button = Button::new_with_label(",");
        comma_button.connect_clicked(move |_| {
            entry.insert_text(",", -1);
        });
        window.set_end_child(Some(&comma_button));

        window.show_all();
    });

    app.run();
}

In this example, the insert_text() method is called on the Entry field when the comma button is clicked. The first argument to the method is the text to be inserted, and the second argument is the position at which the insertion should occur (-1 means at the current cursor position).