Basics first. You obviously should have an idea on how the algorithm/methodology works prior to usage. The ideas for its usage are usually learnt from competing in rounds. Regardless of whether you gain ratings or not, it should be clear that its always a gain for your experience and ideas. It could, in other words, be said that you learn what works in what situation (in generic terms) and what does not from competitions.

So IMO, you should learn the basics of the algorithms, and then come back to understand how the ideas in the editorials work (or how you worked it out in the competitions!)

Assuming you read a basic algorithm book (say, introduction to algorithms) and you know very basic combinatorics, number theory, and group theory, perhaps you just need to learn segment trees. Then you are good to solve any problem for div2. You don't need to study a lot; it's more about problem solving skills/abilities.