Example of using a screen manager with buttons to switch between screens in kivy

main.py

from kivy.app import App
from kivy.uix.widget import Widget
from kivy.properties import StringProperty, ObjectProperty
from kivy.uix.screenmanager import Screen

class MainMenu(Screen):
    name = StringProperty('main_menu')

class OtherMenu(Screen):
    name = StringProperty('other_menu')

class RootWidget(Widget):
    state = StringProperty('set_main_menu_state')
    screen_manager = ObjectProperty(None)

    def __init__(self, **kwargs):
        super(RootWidget, self).__init__(**kwargs)

    def on_state(self, instance, value):
        if value == 'main_menu':
            self.screen_manager.current = 'main_menu'

    def set_state(self, state):
        if state == 'main_menu':
            self.screen_manager.current = 'other_menu'
        if state == 'other_menu':
            self.screen_manager.current = 'main_menu'


class TestApp(App):

    def build(self):
        pass

if __name__ == '__main__':
    TestApp().run()

test.kv

RootWidget:

<RootWidget>:
    screen_manager: screen_manager
    ScreenManager:
        id: screen_manager
        current: 'main_menu'
        pos: root.pos
        size: root.size
        MainMenu:
            screen_manager: root
            size: root.size
            pos: root.pos
        OtherMenu:
            screen_manager: root
            size: root.size
            pos: root.pos
    
<MainMenu>:
    screen_manager: self.screen_manager
    FloatLayout:
        Button:
            text: 'Start'
            size_hint: (.4, .2)
            pos_hint: {'x': .3, 'y': .4}
            on_press: root.screen_manager.set_state(root.name)

<OtherMenu>:
    screen_manager: self.screen_manager
    FloatLayout:
        Button:
            text: 'Other'
            size_hint: (.4, .2)
            pos_hint: {'x': .3, 'y': .4}
            on_press: root.screen_manager.set_state(root.name)