There is only one thing you need to have installed that you might not have already, and that is Python. Python is the programming language in which Atropine is written.
To use Atropine, you need Python 3 installed. At the time of writing (October 2019), the latest version of this is 3.8.0. If there's a newer version by the time you read this, then install that.
Historical note: Earlier versions of Atropine needed the Python module "pygame" for the public-facing screen. pygame is no longer needed. If you already have it installed then you don't need to remove it, but you don't need it.
Older versions of atropine used Python 2. Starting from version 1.0.0, all atropine releases will be for Python 3, and only for Python 3. The rest of this help will assume you are using Python 3.
After you have installed Python 3 as above, unzip atropine.zip into a folder of your choosing. There are a number of files and folders, but the only one you need to know about to use Atropine is atropine.py.
Atropine is a web server. When you run it, you leave it sitting in the background and then use your web browser to connect to it and administer tournaments. To start atropine, run atropine.py. The Windows Firewall might tell you it has blocked some features of Python and ask you what you want to do about it. You need to allow Python to use at least private networks.
Once atropine.py is running, use your web browser to visit http://localhost:3960. This will redirect you to the home screen.
Once you've got Atropine running, you can set up your first tourney.