MediaWiki Administrator's Handbook/Introduction
Sysops, more commonly known on various projects as administrators or custodians are users that have access to restricted software tools used for maintenance. These tools are not available to all editors because the tools can be used to create a rather more serious level of disruption than the generally-available editing tools. It's important that a track record of good-faith editing be established first before granting adminship.
The different Wikimedia projects have different ways of vetting users who request the tools. On most projects this is done through an election process, but new projects (which do not have any bureaucrats, who have use of the "makesysop" tool) need to make the requests on Meta, and at least some projects (such as en.Wikiversity) use a mentoring system rather than open elections.
Getting to know how the tools work is fairly easy, as for the most part they're quite intuitive thanks to our thoughtful developers and years of trial and error. Knowing how and when they should be used is a different issue, since there are a lot of things that should not be done, and each wikimedia project will have different policies and guidelines regarding their use.
The golden rule is simple: never use an administrative tool unless you are sure it's the right thing to do. If in doubt, just leave it to a more experienced administrator, or just ask for advice.