Here is a copy of my jenkins config for running RSpec tests of a Rails app in Jenkins:
[ -d jenkins ] && rm -rf jenkins
mkdir jenkins
cp ~/configs/yourApp/default-db-config config/database.yml
rake db:migrate
rake db:test:prepare
export RAILS_ENV=test
export SPEC_OPTS="--no-drb --format documentation --format html --out jenkins/rspec.html"
rake spec
First it deletes any previous test history from the workspace if it exists.
Next it creates a jenkins directory in the workspace for storing the test output.
Then it sets up the app for testing with a working DB config (I don't store DB config files in my git repo).
Finally it migrates the dev DB if required, prepares the test DB, sets the RAILS_ENV to test and runs the tests with the specified SPEC_OPTS.
The important bits are as follows:
--format documentation ... this sends sensible output of test progress to your console log. Write your tests properly and this will be infinitely more useful than any puts commands you might have considered using.
--format html ... this outputs HTML files of the test results to the jenkins directory created earlier and specified in the --out attribute. Add the following to your job description to show those results on the main page of this job:
<iframe src='http://jenkins.your-domain.com/job/your-tests/ws/jenkins/rspec.html' width="100%" height="600" frameborder="0"/>
Hopefully that should get you up and running with a more useful jenkins test job for RSpec.