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.exe. The installer will prompt installs of any necessary prerequisite software such as the .NET 4.7.2 Framework. 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 with the Microsoft .NET 4.7.2 Framework or newer installed. The installer will prompt to install the necessary .NET Framework if you don't already meet requirements.
Planetary Management may be executed through any HTML5 capable browser.