I can't say that this is the 'best' introduction to Kripke models (as 'best' is always a relative term), but John P. Burgess's survey article "Kripke Models" presumes only knowledge of propositional and predicate logic. It can be found in Alan Berger (ed.), Saul Kripke, Cambridge University Press (2011), or on the Web at www.gauss.ececs.uc.edu/Courses/c626/reports.Kripke1.pdf . It covers most basic applications of Kripke models to modal logic adequately except for the application of Kripke models to forcing. A nice introduction to that topic might be the references in the comments and answer to the mathoverflow question, "Forcing is Intuitionistic". Also the Wikipedia entry, "Kripke Semantics".

I can't say that this is the 'best' introduction to Kripke models (as 'best' is always a relative term), but John P. Burgess's survey article "Kripke Models" presumes only knowledge of propositional and predicate logic. It can be found in Alan Berger (ed.), Saul Kripke, Cambridge University Press (2011), or on the Web at www.gauss.ececs.uc.edu/Courses/c626/reports.Kripke1.pdf . It covers most basic applications of Kripke models to modal logic adequately except for the application of Kripke models to forcing. A nice introduction to that topic might be the references in the comments and answer to the mathoverflow question, "Forcing is Intuitionistic". Also the Wikipedia entry, "Kripke Semantics".