On the desktop of Windows 10, Cortana takes the form of a search box located right beside the Start button. The box will allow you to search the web and your local computer, with results popping up above it. Cortana can be used to perform simple searches, but as on Windows Phone, it can also be used to surface much richer information, like flight statuses. Cortana can also be used to send and dictate emails, control music, and launch apps. Notifications will also pop up here.
Microsoft also showed screenshots of what Cortana will look like on smaller devices. Rather than popping up from the task bar, Cortana takes up the entire screen with a clean white display. Anything that you ask Cortana to do will appear in large text across the screen, with big buttons letting you accept or decline what the assistant believes you want to do. Microsoft's preview of Cortana on smaller screens was limited, but it appears to be fairly similar to what's already out there on Windows Phone.
Cortana will be rolling out to people testing Windows 10 over the next several months.