I trim just the hard fat off the bottom or fat cap, leave the rest, but on the meat side, I will trim as much fat off as possible to expose as much of the meats surface to seasonings and smoke. The following is my recommended method for smoking briskets, there is no "1" right way to cook anything, everyone has their own style, thats what makes BBQ and cooking in general so special.
In general, 225 to 250 pit temp works just fine, smoke with your choice of any number of woods, oak, hickory, pecan, mesquite, cherry, apple or a mixture works well. Fat side up or fat side down, everybody has their own way, but the most important factor is your smoker, try and place the brisket on the smoker where the meats surface is protected from the heat source, using the fat cap as a shield from direct heat on the meat surface. Smoke for 4 to 6 hours until the IT reaches 160 to 165 or you get that nice, mahogany color to the meats surface. Wrap in foil or butcher paper your choice once the IT has reached 160 (if your not a wrap guy, at the very least pan it at this point to catch and save the precious juices that will begin to come from the meat as it enters the stall, these juices will come in handy later for vac sealing leftovers or if your brisket turns out dry), continue the cook until the meat reaches 190 IT, at this point start probing the flat section (thin, lean end) every 30 minutes or 5 degrees of IT increase, until a toothpick or probe can be slid in easily, like probing a tub of butter. In my experience, most briskets won’t become probe tender until around 205 IT, but everyone cooks a bit different. Once you have reached this point, pull the brisket from the pit, vent the foil or other wrap for about 10 to 15 minutes to allow the cooking to stop and the excess steam to escape, wrap in foil or foil pan if it is not already, place in a cooler wrapped in towels for at least an hour, 2 or more is better. Once the IT of the meat has dropped down to 160 or below (optimal temp for the juices to have been redistributed through the meat), it is time to slice it and enjoy. If your slices tend to be a bit dry, simply dip in the au jus or place the slices in a pan and drizzle the au jus over the slices, this will both enhance the flavor and assist with the moisture.
Have fun and most all have patience!
Any number of rubs will work well with brisket, from a simple salt, pepper, onion and garlic mixture to a complex rub like my Texas style rub: 4 parts kosher salt, coarse black pepper, brown or turbinado sugar, then accent with 1 part each onion powder or flakes, granulated garlic, then ½ part each of cumin, chili powder and cayenne. Any commercial steak seasoning will complement the natural beef flavor as well.