I've downloaded the tor browser (Windows). Now where do I go from there and how do I actually open the browser? I see the browser-download is in my map of downloads, but nothing happens when I try to "open" the download. There was also nothing that popped up when the download was finished.
Make sure you downloaded the version for Windows and not for other operating systems.
You can make sure you downloaded the file was not changed and you downloaded it correctly with checking its signature: https://www.torproject.org/docs/verifying-signatures.html.en
The follow this guide to install it: https://www.torproject.org/projects/torbrowser.html.en#windows
You need to run the file you downloaded. If it doesn't run when you double click it, maybe your antivirus is preventing it from running. Check with your antivirus to see how to tell it to let you run it.