Louise asked me about this, in a blog comment. Interesting question. Few ask it, so here goes... :-)

When you hear dog-whistle language, the first thing to remember is that it is intended for ... the dogs.
Don't respond emotionally. Although they get some food and water, the dog-fighting business is NOT run for the benefit of the dogs. Their injuries and deaths are just a cost of doing business. Don't get goaded into the fight.

Be pragmatic. I read/listen to a lot of people I agree with on some topics and strongly disagree with on others. Most people cannot do this. Any bit of difference is a deal-breaker. Compartmentalize what you can use from what you can't use. Don't let the dentist work on your car; don't let your car mechanic work on your teeth.

Don't get news from TV; learn to ask the right questions. Once you realize that most of what is broadcast is directed to the bottom 80% (and designed to keep them there), you should start to ask "What is the intended reaction to this info?", "What info am I NOT getting?" IMO, the bias of the media isn't so much liberal or conservative -- the "bias" is the incompleteness of the info. At best, you get just enough info to make you take the exact wrong course of action (no better time to buy a house ...). At worst, you get told that toxic toys and poisonous food are ok, as long as they're cheap. 

Go to the best sources available and read a lot. Want to make a point about a bill, policy, or speech? Do your best to hunt down a dot-gov or dot-edu source. This puts you ahead of the 80% of people who won't do this.
Some blowhard republican going on and on about Abe Lincoln "freeing the slaves"? It has a lot less altruistic ring to it once you've read Lincoln's letter to Horace Greeley. A northern democrat wagging their finger at "southern" racism has some explaining to do if you ask them about all those northern "sundown towns" and racially restrictive real estate covenants of the past.
Here's one to try out on your own, why did MLK march in Selma, Alabama, but refuse to march in Cicero, Illinois? ;-)

Don't be emotionally owned by either party. For what they have become, they can both be wiped to the dustbin of history for all I care. Neither party cares about the citizens, we are only points to be scored during a game called Election Day. Both their team slogans may as well be "Support us; our brand is less $#!tty than the other brand".

That's the short version, anyway.
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"Racism is not an excuse to not do the best you can." -- Arthur Ashe
"Don't believe them, don't fear them, don't ask anything of them" -- attributed to Aleksandr Solzhenitsyn
"It's time now for you and me to stop running away from the wolf right into the arms of the fox, looking for some kind of help." -- Malcolm X.