Instagram's dark mode is responsive to the iOS or Android system settings. If you have dark mode enabled on your device, when you get the new Instagram update you should see that the app automatically switches to a black background with white text. Twitter's iOS app, however, works differently: you can set it to correspond to system-wide dark mode settings or you can enable dark mode manually.
To enable dark mode on your iPhone, go to Settings, then Display and Brightness and select Dark. There's also a toggle to enable Automatic mode in which your iPhone will change to dark mode at night and go back to light mode during the day.
To enable dark mode on your Android device, go to Settings, then Display, then Advanced and then select Dark from the Device theme menu.