To install Jenkins using Docker, first pull the official Jenkins LTS image with 'docker pull jenkins/jenkins:lts'. Then run it as a container in detached mode with ports 8080 and 50000 mapped using 'docker run -d -p 8080:8080 -p 50000:50000 --name jenkins jenkins/jenkins:lts'. This starts Jenkins inside the container. Next, open a browser and go to http://localhost:8080 to access the Jenkins web interface. Finally, complete the initial setup wizard to configure Jenkins for use. Mapping ports is essential to access Jenkins and allow agent communication. The '-d' flag runs the container in the background so your terminal stays free. The process ends after finishing the setup wizard in the browser.