You can find the font files at https://github.com/cormullion/juliamono/releases.
On that Releases page, you can download:
JuliaMono-ttf .zip|.tar.gz - just the TTF font files, in either Zip (.zip) or Tarball (.gz)
JuliaMono-webfonts .zip|.tar.gz - just the webfonts (WOFF2), in either Zip (.zip) or Tarball (.gz)
JuliaMono .zip|.tar.gz - both fonts and webfonts (TTF and WOFF), in either Zip (.zip) or Tarball (.gz)
(I wouldn't recommend cloning the git repo, unless you want to download over 1 GB of outdated files and git diffs...)
The raw source files (in Glyphs.app format) are at https://github.com/cormullion/juliamonomaster. You'll need a licensed copy of Glyphs to build the font from these files.
To install and activate a font, launch Font Book from your Applications folder, and drag the font files into the middle pane labelled Font. If you're using a different font manager, you already know what to do. :)
On the latest version of Homebrew, you can install the fonts with:
brew tap homebrew/cask-fonts brew install --cask font-juliamono
You can install a font for a single user or for all users. (Some applications (such as Java) don't see fonts unless they have been installed for all users.)
To install and activate a font on Windows, go to Computer |> Local Disk (C:) |> Windows |> Fonts. Locate the expanded .zip file folder, and drag the font files from there into the Fonts folder.
To install for all users, just right-click the font file(s) and choose Install for All Users. Administrator privileges are required.
You might want to install Font Manager:
sudo apt install font-manager
Then double-click on the font files and click Install on each one.
For Arch Linux, there is also a package in the AUR.
Locate your font folder. Might be one of:
~/.fonts /usr/share/fonts/truetype/newfonts/ ~/.local/fonts/ ~/.local/share/fonts/
and copy the files there. You might want to (or have to) regenerate the font cache:
$ fc-cache -f -v
And verify installation:
$ fc-list | grep "JuliaMono"