We built Simplenote so that you should never have to force a synchronization to happen. In most circumstances it will happen automatically and you don't have to press any buttons.
But if you really need to, you can still perform a manual sync. On iPhone or iPad, make sure you're in the main list view (you might have to press the Back button first), and press the Settings button. Then press "Sync Now" at the bottom of the screen.
In the web app, simply refresh your web browser to force a synchronization.