I’ve posted a couple of good articles about propositional logic and the use of tableaux in proofs. The first is a great article by Mordechai Ben-Ari called
“Propositional Logic: Formulas, Models, Tableaux”
The second is a set of slides on tableaux from Paolo Liberatore’s course on automated reasoning:
http://www.dis.uniroma1.it/~liberato/ar/tableau/tableau.html