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.
You can make a pickled beef without the pink salt, but it won't be the distictive color and the texture will be different as well.
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 corned beef) 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.
Right now, I've got my beef resting comfortably in the fridge in the brine. When I get to cooking, I'll post that recipe and the final results.