How can you develop great IT operations skills?

To develop any skill you'll need2 things1.
Knowledge2.
Practice For the Knowledge, I highly recommend that you go with ITIL.
One of the5 main areas in ITIL is Operation.
It illustrates well-known world-wide recognized standards for IT Service Operations.
Meanwhile, try to apply what you learn gradually at your work.

1. Through work experience
2. From knowlege and best practise methods
3. Read it from experienced professionals and
4. certify the similar courses to improving the knowlege and process

You can develop the skills while working.