How do you identify the state and transitions in a DP problem?

The state defines what information you need to uniquely describe a subproblem. For the climbing stairs problem, the state is the current step number. For the knapsack problem, the state is the current item index and remaining capacity. Transitions define how you compute the answer for a state using previously solved states. For climbing stairs, the number of ways to reach step n equals the ways to reach step n minus one plus n minus two.