First set up environment variables to tell Ruby and Gems where to find stuff:

export GEM_HOME=$HOME/lib/ruby/gems/1.8
export RUBYLIB=$HOME/lib/ruby:/home/ian/lib/site_ruby/1.8

Download and unpack the Gems source (this is the version I downloaded, you should grab the latest:

wget http://rubyforge.org/frs/download.php/20989/rubygems-0.9.4.tgz
tar xzvf rubygems-0.9.4.tgz
cd rubygems-0.9.4

Run the setup.rb script with the right arguments to install into your home directory:

ruby setup.rb all --prefix=$HOME --siterubyver=$HOME/lib/site_ruby/1.8

This will install the gem command (and a couple of others) into $HOME/bin and the Gems source into $HOME/lib/site_ruby. Gems will be installed into $HOME/lib/ruby/gems/1.8. You should add $HOME/bin to your path. If you want to install it somewhere else replace $HOME with the prefix you’d like to use.