Installing Jenkins Locally
Let's install Jenkins locally using docker.
docker run -p 8080:8080 -p 50000:50000 jenkins/jenkins:lts
You should see some initial setup happen, and it will tell you what your temporary admin user password is.
Visit localhost:8080, and you'll be prompted for the temporary password. Create a new user account. You now have a working Jenkins server running locally.
Initial Thoughts
I was able to create a New Project. I named the project, and I set it's remote repository url to a repository running on my local git server. I set the build trigger to be "GitHub hook trigger for GITScm polling", which I assume will cause a build whenever code is pushed to the repo. I then setup a simple build action to execute a shell script. I saved that, and then I was able to manually run the build by clicking "Build Now". Afterwards, I could view the console output for the shell script.
Since I set the remote repo, I was able to view the project's files inside of Jenkins. This is labeled the project's "Workspace."