How can a Sys. Admin skill up to work as a DevOps engineer?
Have a look for DevOps Engineer roles and check out the list of technologies that they are seeking. Typically you'll need automation scripting skills (like Bash, Python or PowerShell), configuration management skills (like Chef, Puppet or Ansible) and some fundamental experience maintaining and configuring a Build/Release pipeline. For this, look to get experience with CI/CD tools like AppVeyor (.NET), Jenkins, Travis CI etc. You should also be familiar with Git and source control systems in general such as BitBucket or TFS. You would also benefit from becoming familiar with automated testing techniques.

If you haven't already, consider hosting some open source products in Github and setting up a pipeline for them that performs automated tests on commits as well as (if possible) publishing to a package management system. This is great experience as well as demonstrates your skills.

For a more general understanding of the philosophy of DevOps (as beware that it's a culture as well as a technology set) do as much reading as you can on the topic and start following (e.g via Twitter) the likes of Gene Kim, Jez Humble, and Patrick Debois. Also I recommend you read The DevOps Handbook which they authored. It is a very thorough explanation of what DevOps is as well as how organisations might adopt it.

You could also check out DevOps related Meet Ups and Conferences (such as Velocity, DevOpsDays and Config Management Camp). The opportunities will of course vary depending on where in the world you are.