This feature is really a dud at the moment. Project My Screen works via Miracast, and will require OEM firmware updates to function properly. So Lumia users won't be seeing it until at least Nokia Cyan.
Also, Joe Belfiore warned that most current generation hardware wouldn't be compatible, and that the 1520, Icon and Ativ SE /might/ have it enabled. This is puzzling, as the chipset running on all Lumia models is indeed Miracast compatible on Android models using the same chips. Yes, Nokia would have to update the firmware to enable the feature, but it /should/ be compatible. The likely explanations are that either Lumias are using custom chips that aren't compatible with Miracast, more likely that Windows Phone simply can't handle Miracast on these chips (for whatever reason), or most likely: Belfiore is just mistaken.
We'll likely find out when Nokia Cyan comes out. But we won't see Project My Screen be useful for quite sometime, until OEMs start pushing out the necessary firmware to enable it.
As for a USB connection: this will require a application download from Microsoft. It will run on Windows 7 or Windows 8.X, and this software will be required to mirror your device via USB connection.
Project via USB is an OS feature, and so it likely won't require new firmware. It will however, require the new application that Microsoft will make available for download in the coming months.