Start by operating production systems. You will rapidly discover that patching is not a technical issue (as I already said last time there was a patching discussion on HN). Patching is technically "easy".
But if the business does not prioritize (and allocate time towards) patching (and testing that systems work with after) patching won't get done. There are features to develop and deadlines to meet and new systems to turn on and old systems to retire and oh-my-god don't touch those servers otherwise the vendor will not support the prod environment anymore (no longer certified, yay!) and it costs us 30000$ to get certified again.
Too many times I see HN assuming that everyone is running on a public cloud with B/G deployments and immutable infrastructure you can rebuild and redeploy easily. Unfortunately that's not the case.