If you purchase online, you'll get an e-mail with step by step instructions on how to download the game.
Here are those instructions copy/pasted from the sales e-mail. see if you understand

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Thank you for ordering Sins of a Solar Empire!
To install your game you will first need to install Stardock Central (SDC) from the URL above. After youve installed the application, please follow these steps:
1) Along the left-side of SDC, click Games.
2) Now, in the lower-right corner of the screen, click Registration Info.
3) From the dialog box, select Sins of a Solar Empire from the Product dropdown menu.
a. Enter your Stardock.net email address (the same as you used during installation of SDC). In order to prevent problems, its wise to make your Stardock.net email address the same as the one you used while ordering.
b. Next copy and paste your serial number above into the Serial Number field.
c. Click OK to exit the registration dialog.
4) Once registered, Sins of a Solar Empire is tied to your Stardock.net account - so you shouldnt have to enter your serial number again if you ever need to redownload the game.
5) The Games list should now refresh and display Sins of a Solar Empire under Purchased Games in the main right-side window frame. If it doesnt appear, please click F5 to force a refresh or restart SDC.
6) Select Sins of a Solar Empire from the list and an Install button should appear beside it. Click Install and follow the prompts. (Tip: SDC will also allow you to update your copy of Sins of a Solar Empire.)
7) Stardock Central will download all the necessary files and install them to your hard drive. Once this process is complete, just click Run to launch the game or use your Windows Start Menu as you would for any other app.
If you need your serial number sent to you in the future, you can request it via email from the form at:
https://www.stardock.com/support/