My best advice is don’t step up if you CANT STEP UP! I truly believe that leadership is pretty much an innate ability. It can’t be taught. Sure a few good techies can get away with being a supervisor and things will run smoothly. But for the majority, it comes down to their people skills.
Supervising/leading is a social position. Technical pros are the worker bees. Leaders are the ones who know the culture, climate, people, major issues in an organization and are able to step up because it is natural way of doing business for them. These are the people you want to work for- they’re well connected, they see issues coming down the pipe, they know who to pull in for help, they know who to give assignments to, etc.