What I do is identify a technology that I'm interested in and then research it in my brief (and rare) moments of free time. For instance, there may be a new technology or framework that I've been hearing about and I think it'll become useful to me in the future. What I do is get a book (an ebook usually) and then read up on it.
For me, a key is to stick with one subject until I'm ready to move on. I'm rather ADD and keeping things to a single subject helps me maximize the time I spend as well as my typically limited attention span.
I do try to keep my searching for new topics off of work machines because I don't want to be perceived as "that guy" who is always browsing, even if the searching is technology related and worthy of my time.