Did you download it using the GOG Downloader or your browser? If the latter, what browser do you use?

Start -> search -> theme hospital

Search your whole computer for (e.g. press the Windows button on your keyboard, and type the following)

theme hospital

The whole filename is setup_theme_hospital_2.0.0.5.exe.

Run that file in order to install the game, following instructions. After you have installed the game, you can start the game from your Start menu:

Start => All Programs => GOG.com => Theme Hospital => Theme Hospital

or from a Theme Hospital desktop icon, if you let the installer create it too.

EDIT: Ninja'ed

Anytime you download a GOG game, the installer gets sent to a folder in your Documents called GOG.com Downloads.

When you enter the folder, you'll see other folders with names of various games you've downloaded; in your case it might say, theme_hospital.

When you enter that folder, you'll find the game installer, it might say something like, setup_theme_hospital_[some numbers].

When you click that, you'll install the game and have an option to create shortcuts on desktop etc.

Then, after it's done installing, you'll get option to launch game, i.e. play it.

Let me know if that's confusing.