I've got a camera with three pins, two which need to be connected in order to focus, then a third which must be connected to these two in order to fire. Is there some sort of program in which the arduino can "connect" the firing pin and the two auto focus pins after a delay of a certain amount of time, and then repeat?

I think this goes in the interfacing forum.

Its hard to say without more of the electrical details. what might work is to pull the common pin to ground and then AF and shutter wire to highz (direction input, datawrite low) on two different pins.

Then when you want to "connect" the pins to the common pin you can pull them low(direction output, datawrite low).

Be careful though without knowing more electrical details I can't guarantee you won't break something.

Intervalometers are a fairly common application.
Do a search and have a look at the exhibition section.
You'll need some more hardware.