How would I upload and download save data to google drive or dropbox directly from Unity?

That's not as easy as you might think. Google drive as well as Dropbox have their own unique APIs to access their services. Both require a quite complex authentication service. The question doesn't really apply to Unity answers since it's not a Unity specific question. Unity uses Mono and as such It's just a question how you get it done in .NET / Mono. Google has a detailed tutorial for a console application.

The google API consists of several libraries. If they are 100% managed libraries you should be able to copy them one to one to Unity.

For dropbox it should be pretty much the same.

Take a look at this project on GitHub: https://github.com/Elringus/UnityGoogleDrive

It works with all the major target platforms (including WebGL) and doesn't use platform-specific precompiled libraries.