The normal path is to work through the guide until you need to install, but you can skip to installation directly by going here.
The secret is that Elm is just a single executable file. If you are developing a project in ~/Desktop/project/ you can download this file into that directory and run commands like ~/Desktop/project/elm make src/Main.elm or ./elm make src/Main.elm. You just run the local copy of the executable file!
The instructions for Mac and Linux explain how to do this in more detail. You can follow the same steps on Windows, but you need to do each step by hand. (E.g. download the file through your browser rather than with a terminal command.)
The past binaries for Mac, Linux, and Windows are hosted here.
You can download the executable files directly and use them locally.