That's a good question! I do this frequently to brush up on my skills. So what I do is find a tutorial on http://design.tutsplus.com, http://blog.spoongraphics.co.uk, http://vectips.com or http://colorburned.com/category/tutorials/ that's relevant to something I want to learn and I do as much of the tutorial as I can to pick up certain techniques I want to learn. Other times I make Pinterest boards of styles I like or look back at Pinterest boards I made in the past or one's I follow. I pick one that I really like and I copy it the best way I know how to just to get a feel for the style, spacing, colors, layout, etc. When I'm copying something, I notice certain little details that I didn't think of before. And then I just trash it, but I keep the skills I learned with me forever.

I find myself copying a lot of work as well. Copying is more useful to me than tutorials because it really forces you to look at something with a lot of attention to detail. Often, we THINK we're looking at something and learning from it, but we're really mostly consuming passively. Copying forces you to consider all the elements and concepts that went into a piece of work. Like Victoria said, you're more attune to spacing and proportion, etc...

Aside from copying, I find myself doing a lot of intentional experiments where I give myself certain constraints to work under. So maybe I decide I need to use a certain tool, or I have to render a subject in a different style than I'm used to.

Imo, getting better at visual design is mostly about sensitizing yourself to details that most people take for granted. Any activity that forces you to look hard at something can be a great learning experience. Contour drawing, life sketching, etc... The subject matter isn't at all important – your attention to detail is.

If I have a brief thirty minutes to myself i just relax and enjoy them. A calm happy mind produces better work...