I do this all the time, should be simple.
First download the deb from
http://pkg.jenkins-ci.org/debian/
then in a console run
sudo dpkg -i jenkins_1.xxx_all.deb
after that jenkins starts, or you can start/restart with
sudo service jenkins [re]start
To configure jenkins (PORT, JAVA_ARGS, etc.) look at
/etc/default/jenkins, if you modify
don't forget to restart the service.
A later upgrade with dpkg -i jenkins_1.yyy_all.deb should respect
your configuration if there
are no conflicts, otherwise you'll get the resolver as usual with
dpkg
Regards
Felix