You are about to enter the wonderful world of Charcuterie, the preserving and curing of meats.
The traditional cut of beef to turned into corned beef (or pastrami, which has a similar preparation) is a well-marbled brisket. I'd imagine that a flank steak or other similar long-and-moist cuts would work out too.
The curing process involves soaking the brisket in a brine of pickling spices (for flavor) and Sodium Nitrite, which will preserve (cure) the meat and provide that wonderful pink color. You'll have to plan ahead, as the process takes about five days. I've used the recipe detailed in this forum post with fantastic results before. I think that it comes from this book, which you might think of picking up if you have future dreams of sausage, pastrami, and other feats of meat.
Saltpeter is potassium nitrate, which does not directly cure meats. Bacteria convert nitrate into nitrite, which is the real preservative. Saltpeter can be replaced by a smaller amount of nitrite to get the same curing effect (most commercial cured meats do this), though a prolonged cure that converts nitrate into nitrite can develop more flavor.
Tender Quick is not a direct substitute because it contains mostly salt. I've heard that you can replace the salt in your recipe with Tender Quick, and drop the saltpeter, and have a success. You would have better luck finding a recipe that was meant to use Tender Quick, though.
It is definitely possible to buy (food-grade!) saltpeter. I would check online, or at specialty stores. It's a little more difficult than picking it up at your local grocery store, of course.
(Chemistry lesson, courtesy of McGee: nitrate (NO3) is converted to nitrite (NO2), which then reacts to form nitric oxide (NO), which bonds to myoglobin in the meat, which turns it pink and prevents oxidation. Nitric oxide is also present in smoke, which gives that "pink ring" around the outside of smoked meats.)
Best Answer
Consider the flavor of canned corned beef as similar to freshly cooked brined corned beef, with these exceptions:
I just Googled, you're right, very little info. I do not home can, so I can't provide a lengthy answer. I found a historical recipe here, Ball Blue Book of Canning and Preserving Recipes:
Note: That recipe will not provide you with something similar to commercially canned corned beef. It will be a jarred liquid and chunks, it might be better than canned.
For information on commercial canning, Google the term: corned beef retort. A retort is what commercial canners use to sterilize canned products.