From readme mirrored on 2017-02-01 from 1 (on GitHub -- it makes you run non-free scripts, and encourages poor licensing practices).

git clone https://github.com/rbenv/rbenv.git ~/.rbenv
cd ~/.rbenv && src/configure && make -C src
echo 'export PATH="$HOME/.rbenv/bin:$PATH"' >> ~/.bash_profile # or ~/.bashrc
~/.rbenv/bin/rbenv init # Run for shell-specific instructions on how to initialize rbenv to enable shims and autocompletion.

Restart your shell so that PATH changes take effect.

Now check if rbenv was set up:

type rbenv

The readme was in public domain, but this page is released under GNU GPL v3 or later.