There are several ways you can connect an Arduino to a DSLR so that you can use the Arduino to activate the shutter. I chose to use an optocoupler, sometimes called an optoisolator.
Optocoupler
There are many types of optocoupler and you chose one based on the requirements of your circuit. My circuit is a 5V Arduino and a Canon 40D which has about 3.2V on the shutter release. Due to the relatively low voltages there are many suitable optocouplers to pick from. I already had a Fairchild 4N26 so this is the one I used.
4N26
Optocouplers are digital switches. They work by using an LED emitter paired with a photo detector transistor. This means they can be used to allow one circuit to switch a separate circuit without having any electrical contact between the two. Basically, if you put a current through pins 1 and 2 and light the LED the photo detector transistor detects the light from the LED and allows a current to flow through pins 5 and 4. No current on pins 1 and 2 means current does not pass through pins 5 and 4.