Since disjunctions (and negated conjunctions) make weak claims, the most general forms of reasoning about them are not simple; but there are simple patterns of argument involving them that work in special cases.
4.3.1. Detachment rules
If we add to a disjunction the information that one of its disjuncts is false, we can conclude the other disjunct; and a related principle applies to negated conjunctions.
4.3.2. More attachment rules
A disjunction is entailed by each of its disjuncts; and, while this does not provide a safe way of planning to reach a goal, it is a useful way of adding to inactive resources. Again, a similar principle applies to negated conjunctions.