Push RHS of production onto stack, with front end of RHS on top. Provides a nondeterministic algorithm for parsing. Controls exactly when can accept. Good in-class example for proof details. The exact construction and proof is not that important.
Proof provides good example of strategies and ideas.
By definitions of acceptance. By observing initial and final transitions from previous statement. Sufficient for proofs of both implications. Again, makes good in-class example. Proof by induction on length of derivation.