You can sign up for a new account at https://beta.stellaremperor.com/Account/Sign-Up. Sign up is currently free and requires an email address.
The client installer can be downloaded at https://beta.stellaremperor.com/StellarEmperorClient/StellarEmperor-win-Setup.exe. There may be various updates throughout the beta phase, but updates should be delivered automatically.
The Stellar Emperor client currently requires a PC running Microsoft Windows 7 or newer.
Planetary Management may be executed through any HTML5 capable browser.