My experience with this changed a lot when I transitioned from graduate student to more experienced researcher. In earlier days, I followed the advice of starting at the beginning and working systematically through a big work. An example for me was Wall's book Surgery on Compact Manifolds, which is daunting and hard, with some chapters particularly rough going. I didn't succeed in reading it front to back, but I'm not alone. (In the introduction to the second edition, Ranicki wrote "…I always had it with me on my visits home, and once my mother asked me: ‘Haven’t you finished reading it yet?’".)
In more recent years, time constraints meant that this approach was harder to achieve, and usually I had a better idea of what I was looking for. So I would read what I needed to get started, and then go back repeatedly to fill in details (or even major points) as needed for further progress. A prime example for me was the series of papers, Spectral Asymmetry and Riemannian Geometry I–III of Atiyah–Patodi–Singer, which are daunting for the sheer amount of ideas they contain. I think I wrote 3 papers related to the $\eta$-invariant (from those papers) before I finally read the full proof of the main theorem.
For a great description of how to learn in this somewhat circuitous manner, I suggest reading the introductory portion of a beautiful article in the AMS Bulletin, "Harish-Chandra and his work", by Rebecca Herb. The author describes how she was led into his difficult work by her advisor, and found a thesis problem by starting with a single page and ‘working backward and forward’. Of course, it helps to have a good advisor!
