Find where 55-60 degree water intersects the bottom and run your baits close to the bottom. If you can find that with some structure associated with it, all the better. Run your baits on long leads. Like 60 to 80 foot for mono/flouro and lead core setups to match your depth. Slide divers work well for Browns, but don't be afraid to run a standard diver if you don't have slide divers though. Browns can be very aggressive at times, yet very weary most of the time.
I have had success with many different types of baits for Browns. Cranks like Hot-n-Tots, Shadraps, Flicker shads, and even smaller J-plugs have done well. Smaller spoons like Stinger Scorpions in colors like Gold Monkeypuke, Helmut, Purple Pooh Bear, and Razberry Dolphin are some good ones. Copper and Gold blanks seem to work best for me. I've caught them trolling with casting spoons like Cleos, Krocodiles, and KO wobblers as well. Some of my biggest Browns have come on 0 size dodgers with 2" flies behind them, or fly/spin-n-glo behind running on short setbacks behing riggers running right off the bottom... just like I use fishing for Lakers.
In the colder months if you find a warm water discharge into colder water, the Browns will be there. If you find them where they are actively feeding you can have a blast just anchoring and casting spoons, cranks, jigs, or blade baits to them. They fight like the crazy, and can be quite memorble on lighter spinning tackle.
Good luck and hope this helps you get your first Brown!