I forget where I read this but someone did a post about how the best career advice you could give a young kid starting out is for them to identify a senior person’s pain point and offer to take that work away from them. Not only is it perhaps the single best piece of career advice I’ve ever heard, but it’s applicable to everyone at pretty much every level, not just someone coming out of school.
Figure out what portion of daily drudgery people need to have out of their lives and offer to to take it off their plate. This can be boiled down to “Make yourself useful,” which is the first thing my wife says to me when I open my eyes on Saturday mornings.
I would venture to guess that some of the most successful people working in businesses owned by others began this way. “Tell me what you need done, I’ll make it my daily mission to do it for you, freeing up your time for bigger things.” Say that to your superior or to the boss herself and just watch what happens – for both of you.