You probably already had this conversation with Walter, but...
Knowing which brake is on which side is pretty important. The rear brake is a lot safer, though at some point it locks up the wheel, and there's no more braking available in that department. The front brake is way more effective, but somewhat risky, because if you have enough speed or are going downhill, it can send you over the handlebars, and also, if you lock up the front wheel, then you lose your ability to steer/balance, even if the wheel is sliding. (Unlike locking up the rear wheel, which is often a useful technique on short steep descents.)
Normally the rear brake is on the right, which is easy to determine by looking to see if the brake cable from the left brake lever goes to the front brake. If, as a southpaw, you would find it more convenient to have the safer brake on the left, they can be reversed without much trouble. (This will also provide great entertainment if anyone borrows your bike.)
I can't believe Peter was serious when he said he didn't know which side was the front brake. On my road bike, I use my front brake about once or twice a year; and I would never apply it until after I had already applied my rear brake (since if I use it, I'm going down a steep hill). But the few times I have used it, it was a good thing I had it :-)
I always use my front brake, and generally feel perfectly secure doing so. I can't recall ever having a problem with it. There are times when I use both of them, but not all that often unless I am going down something particularly steep, and I think it is probably pretty rare for me to use my rear brake only.
Road bike is a different story, and using the front brake is no problem unless you do something radical.
I also tend to use front more than rear (road/gravel) and actually have the levers reversed to put the front brake on my stronger hand (mostly for cold weather reasons)
I've always had the front on the right side, also my stronger side. First occurred to me after riding with Jim Pike and others from work. He was one of the top riders in CT at the time. If good enough for him.... In fact his back brake was just wide open so may not even have made contact if he tried.
Hmm, going down some dirt roads today at 25-30 mph with the potential (but not the wish) to go a lot faster, I was taking advantage of both brakes. And disc brakes don't really care which your stronger hand is as it doesn't take much strength to make them grab a lot more than you really want.
I did check, it seems the right hand works the rear brake. :-)
For British bikes, it's reversed, supposedly having to do with driving on the left, and so doing more left turns than right.
For road bikes, I find the back brake is better for regulating speed, just shaving off bit heading into a corner. Of course, the front brake is better for stopping, especially stopping in a hurry, but my goal on any bike ride is never to stop and have to unclip. That's why all my routes go clockwise.
Part of an amusing long story: I was finally heading back down the dirt road from Gold Hill toward Fourmile Canyon on my recumbent in the fading light. It was a delicate balance, because if I applied too much rear brake, the rear wheel would lock up on the loose surface and I'd keep moving but the light that was powered by a generator on the rear wheel would go out and I couldn't see. But if I applied too much front brake (which was really easy to do since the weight is so unevenly distributed toward the back) the front wheel would lock up and I'd fall over. I definitely should have started earlier.
We were riding in very fast pace lines back then. If you were in the line, you almost always riding the brakes slightly to prevent touching the wheel 4-5" in front of you. No brakes if you were in front our sliding to the back and hoping to hook back on. I found I had better control, or adequate control, with the right on the front.