I'm about to install several Hunter ceiling fans. This will be the first time I've done anything electrical past changing a bulb. The instructions that came with the fan show three wires coming from the ceiling box for a single switch light. When I remove the light, there are only two wires leading to it. And the wires are old, cloth covered. (House was built in '50.) Why two rather than three and what the heck do I do now?
Two is "normal". Black for hot and white for neutral.
Your fan has 3 wires (4 counting the green ground). You will have a white which you will connect to your neutral and you will have power for light and power for fan. Both of the power lines will be capped with your "black"/hot wire coming in.
To have the light and fan controlled independently you would need to rewire from fan to switch with 12-3 (or 14-3). An alternative is to install a remote that has sensor sitting in fan unit (or buy a fan with it built in).
The 3 wires are normally hot, neutral, and ground. It sounds like your home doesn't have a ground wire.
If the box is metallic, there's a chance it may still be grounded, even though there is no wire. There's an answer to a similar question that describes how to check if a box is grounded.
If the box is grounded..
If the box is grounded, then you can connect the ground wire from the fan directly to the box, and the fan will be grounded.
If the box is not grounded, you have two choices:
Personally, if I was unable to get a ground to the box, I'd probably use a fan that was remote controlled so no one ever has a need to touch it (get a fan either with no pull strings/controls, or cut the cords off so no one is tempted to touch them). The wall switch can be left in to control overall power, and the remote used to switch light/fan speed, or the wall switch can be removed so the power is permanently on and the remote is used for everything.
In any case, you should connect the fan's ground wire to the box, so that at least the fan body and box are bonded (at the same electrical potential).
DO NOT CONNECT GROUND AND NEUTRAL in the box. This is sometimes called a "bootleg ground" and is not only pointless, but actually very dangerous. If the neutral wire ever has a fault ANYWHERE, in addition to the fixture simply not working, it becomes energized and you can be shocked if you touch it (as you likely would to, say, check if the light bulb was burnt out).
Just connect the blue and black wires from the fan to the black wire in the box. Then white to white. Or add a damn remote.