You can buy a pickling mix at the grocery store or make your own.
Most store-bought pickling spices don't include hot peppers, so if you want a spicy corned beef, add the red pepper flakes or your choice of hot peppers as desired.
Some recipes add interesting flavors like ginger and cinnamon, but at the beginning you might want to stick with a basic mix.
I've made a few corned beefs (and corned turkey as well) and I'm still fiddling with the details, but this is the current project.
First, you need to buy a brisket. I was lucky enough to find a whole cryovaced brisket at a great price, so I decided to buy that and carve it up myself. But you can buy brisket that's the size you want and use that.
The only required item you might not find at your local grocer is pink salt. This isn't a fancy salt that you sprinkle on food, it's a mixture of salt and sodium nitrite. The bright pink color is added so you don't mistake it for regular salt. You can buy it online from sausage-making suppliers.
You can make a pickled beef without the pink salt, but it won't be the distinctive color and the texture will be different as well. (For more details on pickling with and without pink salt, see my post about what makes corned beef pink - it includes another picking recipe, as well as cooking instructions.)
1 gallon water
2 cups kosher salt
1/2 cup sugar
5 teaspoons pink salt
3 tablespoons pickling spice
2 cloves garlic, crushed
1 tablespoon hot pepper flakes or your favorite hot pepper (optional)
4-5 pound beef brisket
Combine all the ingredients (except the beef brisket) in a nonreactive pot large enough to hold all this, and bring it up to a simmer.
Stir to dissolve the sugar and salt, and when it has been completely dissolved, take it off the heat and let it come to room temperature, then refrigerate it to cool completely. If you're going to need the pot in the next week or so, transfer the brine to a suitable nonreactive container that will hold the brine and the beef comfortably.
Put the beef into the pot with the chilled brine and weight it with a plate to keep it submerged. Refrigerate for 5-10 days. Check it daily to make sure it is staying submerged. Some recipes suggest that you turn the corned beef daily, every few days, or not at all. If the beef is wedged up against the side of the pot, or you think it may have been floating above the liquid, feel free to turn it. Or not.
Also, most recipes give a range of times for the brining process, but none of them tell you exactly what to look for to determine if the beef is done. The best I can tell you is that the beef feels different when it is cured, but it's a little hard to tell if it has brined completely to the center. If I figure out a sure-fire method, I'll let you know. Meanwhile, the best I can say is that if the cut is thick, let it brine a little longer.
In theory, a longer brine shouldn't make any difference, but there's probably some point when quality begins going downhill. Probably not a matter of days, though. This is a preserving process, so if your schedule delays the cooking by a few days, a longer soak shouldn't be cause for concern.
When you're ready to cook it, rinse the beef well under cool water. Cook it as you would a store-bought corned beef.
Need help cooking it? Check out my corned beef in a pressure cooker.