There are a few places to conduct this clean up process. I start by going over the beef brisket and removing any loose pieces of meat or fat. A thin strip of meat hanging off the side is going to dry up and overcook, so there is no point in keeping it.
Once you have the loose pieces off, flip the brisket over on the meatier side. Here you will find pieces of membrane similar to that on a rack of BBQ Ribs. While it isn't necessary that you remove all this, I do find that it can block flavor from getting into the meat.
Now, there is the fat. A whole beef brisket has a lot of it, too much in some places. If you know anything about smoking brisket, you know that the fat keeps the meat moist during cooking and adds flavor as it slowly breaks down. Now the most important fat in your brisket is not the big pieces on the fat cap (the fatty side of the brisket), but the fat inside the meat. These are the small ribbons of fat in the meat that will do the most good. I am not saying that you need to remove all the fat, but you should cut away some of the large, thick pieces. Don't cut down to the meat, just carve off the excess. By doing this you can reduce the weight of the brisket by a pound or two and thereby reduce the overall cooking time.
It is this final weight that you need to use for your cooking time.