Since you have no idea how to hook this up, you should get help from a knowledgeable friend or electrician. I say this because I am concerned about your remark that jostling these wires turns on the fan. Does that mean that the fan turns on without the black wires touching? And is the picture you included a previous location for a switch or what?

Also, do you know what those two cables are and where they go? If one of those cables was power, and other one went to the fan, you would just hook the two blacks to the switch and wirennut the other connections.

However, until you are sure about the function of those two cables and can clarify the issue about jostling the wires, don't do anything.

If there was a switch here originally then there is only one black wire, cut in two for a switch. A white wire cut at the same time and then rejoined, ditto for the ground.

A switch always goes on the black, or power, line.

Jostling the wires (specifically the black ones when they touch) turns the fan on.

The picture is what I assume to be the previous location for a switch for the fan...the previous owners were evicted and left it in a pretty odd state.

Then it's pretty likely that the hookup is as hendricus and I described. In addition to the existing wires, a new replacement switch should have a ground screw and you need to run a bare copper wire from that to the two existing ground wires, and wirenut all three.

My remaining question, however, would be why they removed the switch...i.e., was there a malfunction problem with the fan?

From the tone of the original post I agree that this is probably not within the scope of what the OP can do. Regardless of how simple.

One of those black wires is HOT, so BE CAREFUL. DO NOT go near it until you can get someone in there to fix it.

With that large amount of NM sheath extending into the box, the existing installation (such as it is) doesn't look to me like professional work. I'd question what's inside the walls.

That said ... most likely, to get it working, you'd put wirenuts on the twisted ends of the ground and neutral wires. Then connect the two black wires to a 2-pole switch. The wires go clockwise round the screws on the switch. Tighten securely.

See Wiring Simplified (available at Home Depot or from your public library) for more information on basic wiring.

"Then connect the two black wires to a 2-pole switch."

Single pole switch.

You are only switching one connection.

Yeah, that's what I said. "Single pole switch." :)

Oops. Thanks Brick, my brain missed third gear and ended up in neutral.

use a hubbell spec grade switch. dont settle for a cheapie, they will wear out quickly