The command rbenv install is missing

The install command is not embedded into rbenv, it comes from the ruby-build plugin. You can install it using the command:

git clone https://github.com/rbenv/ruby-build.git "$(rbenv root)"/plugins/ruby-build

On Mac OS X you can install it through homebrew:

brew install ruby-build

On Debian (version >= 7) and Ubuntu (version >= 12.10) both rbenv and ruby-build can be installed using apt-get (or aptitude):

sudo apt-get update
sudo apt-get install rbenv ruby-build

On FreeBSD ruby-build is available in the Ports Collection, it can be install both as a binary package or build from the port:

# Using pkgng rbenv will be installed
pkg install ruby-build

# Building ruby-build form Ports will install rbenv only if the RBENV option is set
cd /usr/ports/devel/ruby-build
make install

I found that when using rbenv from a global directory, it's necessary to export the RBENV_ROOT variable, otherwise it won't load the plugins.

export RBENV_ROOT="/usr/local/rbenv"
if [ -d "${RBENV_ROOT}" ]; then
  export PATH="${RBENV_ROOT}/bin:${PATH}"
fi