Smoking briskets in Texas is like making sausage, everyone has their own way of doing it.
I like to smoke mine for about 2-3 hours, then wrap it in foil for 4-6 hours depending on the size, temp, and number of briskets. I have cooked 1 brisket and I have cooked 1800 lbs of meat. And I have cooked in 105 degree weather and down to 20 degrees with ice on the wood. So time and temp is dependant on many factors.
I could not tell you the exact temp because I have never used a thermometer. I was taught to use my hand on the side of the smoker. It is easier because once you learn you can check any side of a large smoker instead of depending on the thermometer set in one location. But I think it is somewhere between 275 and 300 degrees typically maybe hotter. If you are using a store bought smoker there will be instructions on the time and temp for that model.
I believe rubbing a brisket to be best. My basic recipe has paprika, mustard powder, cayenne, course black pepper (must be course), granulated garlic, and then whatever other spice sounds good at the time. I usually also use a good sea salt. Though many people frown on using salt.
I do not cut much of the fat off of the brisket. But I do cut the "hard" pieces off of it. When you feel the fat there are certain parts of it that are really hard. It is tough to explain in writing, but you will know when you feel them. Though some younger beeves do not have the tough fat. Most cheaper briskets are older cattle though, so you will encounter these peices when buying buying meat on sale.
I never dope my brisket. In other words I never put any type of sauce on it while it is cooking. If you want sauce on it, that is your own choice while you are eating it.
Now the big debate:
Fat side up OR Fat side down.
I am of the fat side down contingent. I believe that as the fat cooks it releases the moisture which in turn becomes steam and makes the brisket tender. The fat gets hotter if it is on the bottom side so there is more steam. Also, this insulates the meat from the direct heat and will cook slower and more uniform. It still gets plenty of smoke.
As the meat cooks, it releases liquid and sits on top of the meat. It keeps it moist until you get it wrapped.
The most important part of cooking brisket is to go slow, and keep it moist in the meat. There is nothing worse than dry brisket. Well, maybe dry ribs.
Also, make sure to drink enough beer so the cooking does not go bad.