First make sure you are using a version control system so you can make
changes and back out if necessary. (I prefer git, some like svn etc.)
Next make sure your test suite is comprehensive so you can be sure you
have not messed anything up.
Install the rails version 2.3.4
Edit config/environment.rb so you have a line like
RAILS_GEM_VERSION = '2.3.4' unless defined? RAILS_GEM_VERSION
It should currently reference the old version.
Then do rake rails:update, it should update boot.rb and probably some
Commit that version to your version control system
Run your tests