Installation

wget -q -O - https://jenkins-ci.org/debian/jenkins-ci.org.key | sudo apt-key add -
sudo sh -c 'echo deb http://pkg.jenkins-ci.org/debian binary/ > /etc/apt/sources.list.d/jenkins.list'
sudo apt-get update
sudo apt-get install jenkins

Upgrade

Once installed like this, you can update to the later version of Jenkins (when it comes out) by running the following commands:

sudo apt-get update
sudo apt-get install jenkins

What does this package do?

Jenkins will be launched as a daemon up on start. See /etc/init.d/jenkins for more details.
The 'jenkins' user is created to run this service.
Log file will be placed in /var/log/jenkins/jenkins.log. Check this file if you are troubleshooting Jenkins.
/etc/default/jenkins will capture configuration parameters for the launch like e.g JENKINS_HOME
By default, Jenkins listen on port 8080. Access this port with your browser to start configuration.

If your /etc/init.d/jenkins file fails to start jenkins, edit the /etc/default/jenkins to replace the line

HTTP_PORT=8080

HTTP_PORT=8081

Here, 8081 was chosen but you can put another port available.