So, I was randomly given brisket. I've never ever cooked anything like this before, any advice on how to do this well, and fairly easily?
Hmm, haven't had brisket in years, but I more or less remember how to do it. The most important thing is to cook it slowly and gently--for example, if oven-roasting, about 4 hours at around 300F for a 4-lb. brisket, until it gives easily when a knife is inserted, should be about right. Also, if you're the type who always trims fatty cuts of meat, don't trim brisket until after cooking; otherwise, you risk it cooking up flavorless and tough. Ideally, it should really be marinated first with whichever seasonings you're planning to use, then after cooking refrigerated for actual serving a day later (very gently reheated), when the flavors have had more time to meld...but you're probably straying beyond "fairly easy" territory at that point.
The classic Southern Jewish preparation for brisket, which was the way I always had it growing up, involves oven-roasting it with Coca-Cola (which tenderizes it very nicely) and a French onion soup-type stock. Pat dry and lightly salt the brisket, give it a nice sear in its own fat in an ovenproof stockpot, remove, drain off most of the fat, then gently saute a couple onions and carrots and several cloves of garlic in the remaining fat, until browning. Add about half a cup of cooking sherry and deglaze (bring it to a boil, then allow to reduce to a glaze, scraping the browned onions and garlic off the bottom as it reduces). Put the brisket back in the pot, along with enough Coke, water, and good-quality soy sauce (a 3:3:1 ratio should be about right) to almost cover the other ingredients. (You could also add, to your taste, some paprika, cayenne, peppercorns, bay leaves, or whatever else you like at this point.) Then cover the stockpot and put it in the oven to roast, checking occasionally to see if it needs more water.
Also, while I've never made the below recipe, only eaten the time-consuming slow-smoked original version, I can vouch for the overall quality of the blog it's from:
Homesick Texan - Oven-Roasted "BBQ" Brisket