To avoid answering questions directly because you don't know the answer, or you don't want the person to talking to knowing the real answer, and talking about another subject you do know something about, or something to flatter or distract the other person, instead. Also resorting to speaking in talking points, folksy colloquialisms, or buzz words to avoid answering questions while trying to look like you know what you're talking about and to keep from having to give an honest or valid answer.
"I didn't do any research for my oral report on raising chickens so I pulled a Palin and started talking about how to make fried chicken."
"I knew that car salesman was full of crap when he pulled a Palin on every question I asked about the car. The last straw was when I asked him about gas mileage and he just said, 'Little lady, I can tell you all day about how few times you'll need to take this pony to the trough but we ought to close the barn door on it before some eagle eye rustles it up from ya. Why don't we just talk about it in the office while I get the papers ready' I ran as fast as I could.
"When I asked my boyfriend
about the rumor he was doing gay porn, he pulled a Palin and mumbled something about my friends trying to pull a smear campaign."
"If he asks you what you were doing afternoon, pull a Palin and talk about your new car and how cute his kids are."