Here are the tools I ended up using the most. You're actually supposed to use a big trowel (which you can see in my mortar bucket up there) but I found it far too ungainly. I'm sure if I were bricking up a wall of 10,000 bricks I'd appreciate being able to slap the mortar onto each one with a big trowel, but I'm just doing detail work here, and I found the smaller one much easier. The slightly S-shaped thing is a jointing tool, used for pushing mortar between bricks and for shaping the joint after the mortar has gotten "thumbprint hard".
I started at the left, and worked right. You can see this, to a certain extent, in the regularity of the mortar. It turns out that working with mortar is hard. My wife said, "I told you it was going to be hard!" To which I answered, "I told you it was going to be possible!" And it was, both.
The finished product, though, doesn't look half bad. It's not terribly straight, but - this is the important point - today, these bricks are no longer falling out. My next brickwork will be better, and this will be basically invisible, once the windowsill is in place.
What I learned about masonry: mortar dries fast. Also, bricks soak in moisture like little, heavy, clay sponges. I used my detergent bottle to squirt water on continually, but a sprayer would be better. I also kept adding water to my mortar in the bucket. It all hardened up fine, so this must have been OK.
You're supposed to put your mortar onto the bottom of the brick, and the end of the brick which will butt up against the last brick placed. When I tried this, the mortar fell off. So instead, I put the mortar onto the bottom, put the brick into place as quickly as possible, then sort of post-tuck-pointed the mortar between the bricks on the sides. Since the bricks are pretty solid today, this must have been OK.
Also, these bricks are actually too close together (not my fault, they're laid that way; I was just putting them back where they were). There were gaps of only about 1/8", instead of 3/8", which is the minimum jointing tool size, thus presumably the minimum normal gap between bricks. Anyway, this made it tough to get any mortar into the gaps.
So my first bricklaying endeavor seems to be at least good enough: the bricks aren't falling out. I call that a success.