Disclaimer: Docker is a way to build applications, it's not necessarily a DevOps thing.
Let me answer this by trying to say what DevOps is all about and how we do it at Hashnode. I'll go into how you can get started with it in the second part of my answer.
All we're trying to do is make sure how fast a change made in your development repository gets shipped to production. Besides the deployment side of things, a DevOps engineer's role is to set up load balancers, make sure the machines are up and if they are down, have a swift backup plan. These things are usually a one time set up thing. Deployments can also be a one time set up thing and we've achieved exactly that at Hashnode.
We have two types of deployment at Hashnode:
You can use any tool that suits you best (please stay away from Jenkins though) to get started with. Build a test project, say a simple NodeJS hello world server. Try to bring it out on a cloud machine and access it over the internet (AWS can be intimidating for beginners, so I would recommend using a simple digital ocean machine). Now, try to check in to code to your repo. Your end goal should be to see it live on your digital ocean machine. The story I had linked earlier in the answer should be a good starting point for you to achieve this.