To start playing Medieval Empires, you will need to create a player account by following these instructions:
https://medievalempires.helpshift.com/hc/faq/15-how-to-create-a-player-account/
After this, download the game for MacOS or Windows from the website.
For Windows, once the setup is downloaded, you can run it from your downloads.
You may get a message, where you would need to give permission to run the app.
Once the setup has downloaded, you can install the game.
For MacOS users, you will need to download the Mac version from the website.
Following this, install the game on Mac (by dragging the game logo to the folder)
Click Open to start the game.
Once you enter the game, simply add your Player Account details and start playing!