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I have the following question and am not sure how to do it.

Find the resolvent for the two clauses:

$P \vee \neg Q \vee R$

$P \vee \neg R \vee S$

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    This looks like a question to make sure that you have read and understood the definition of a "resolvent". Do you have such a definition in your textbook/notes? Please edit your question to quote that definition.2012-11-05

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Resolvent is the outcome of applying the resolution rule. In your case, there is only one possibility how to apply it: $ \frac{P\lor\lnot Q\lor{\boldsymbol R}\qquad P\lor{\boldsymbol {\lnot R}}\lor S}{P\lor\lnot Q\lor S} $