You can quickly add a new event in Teamwork Projects no matter which part of your site that you're currently in, by using the Quick Add button in the top right above the search bar:

You can click the 'Add Event' option, or to speed things up even more press 'Q' on your keyboard to bring up the menu then press 'E'.

When you choose to add an event in this menu, you can use the new event creation window to add all the event details - all without leaving the screen you were viewing.