I think everyone reads cases differently.
When I read a case, I read it the first time through without taking down any notes so that I get an idea of what is going on. I then take down notes according to the following format:
1. Material Facts
Material facts are facts that are "important" in determining the outcome of a case. This is probably best explained by an example. In say a negligence case, someone slipped over at Woolworths and injured themself. A fact can be the victim's name is Sam Smith (made up name). However, that isn't important in determining the outcome of a case. An e.g. of a material fact could be a puddle of water where the victim slipped.
2. Issues
Determine what is currently in dispute or an issue to determined. Using the example above, an issue could be "Is Woolworths negligent?"
3. Decision
What was the outcome of the case?
4. Legal Reasoning
How did the judges come to their decision? What reasons did they give?