Testing a static website was fairly simple. At the most basic you could just curl the pages to make sure you was getting the page expected. A more comprehensive test could be written in Python without any additional modules; although requests and a testing framework makes life easier.
This is where Selenium comes in. This allows you to control a browser programatically, recreating the steps a tester would do manually. The python language bindings can be installed with pip as usual. To control a browser it uses an API known as WebDriver. To actually support the different browsers you need the appropriate WebDriver application for that browser, which can be downloaded from the following locations
Where you have 32- and 64-bit versions, you need the same one as the browser you wish to control, not your OS. So the 32-bit Internet Explorer WebDriver will control the 32-bit version of Internet Explorer. These need to be placed in a folder that is included in your path environment variable so that Python can find and run them; alternatively you can add the folder to sys.path before use. Each WebDriver has a different name so they can all go in the same folder. Although the Microsoft Edge WebDriver is an msi (the others are zip files) it does not add the installation folder to your path. I’ve also found the WebDriver for the last two, Internet Explorer and Opera, to be buggy but your mileage may vary.
Now for a quick test. To demonstrate a few features I’ve uploaded a script to BitBucket that simply checks if this blog is on the first page returned when searched for. This should always be the case but it does demonstrate starting the driver, opening a page, finding an element and inputting to it, then checking the result contains an element you was expecting.
Hopefully this should give you some idea of how to make a start. The official documentation has examples in Python of each call.