If you use a digital, single-lens reflex camera and you want to get your flash off your camera, you have two choices: wired or wireless.
Here are two scenarios and the equipment required:
One flash unit off camera
To trigger a single flash off the camera, the cheapest route is to go wired. You need only your camera, a flash and one PC synch cord. With the release of the shutter, this cord creates an electrical contact between the camera and the flash unit. Most DSLR cameras and stand-alone flashes have PC terminals, although some cameras and flashes vary in their connector style, so make sure you purchase the appropriate cord.
You can purchase these cords in various lengths and in coiled or straight styles. The advantage to the wired option is that there is no way another photographer will inadvertently fire your flash. A good resource for all types of PC cords and connectors is paramountcords.com and FlashZebra.com.
More expensive, but a lot more convenient, is the wireless option. A one-flash setup requires two battery-operated devices: one to act as a transmitter at your camera location, and one to act as a receiver at your flash position.
The transmitter fits into the hot-shoe of your camera, and the receiver connects to your flash. They work by radio frequency similar to a garage door opener, and some advertise a range of up to 1,600 feet under good conditions.
Most photojournalists favor the PocketWizard system where a unit pair will cost about $350. Paul C. Buff Inc. has the less expensive CyberSync products that start at $130 for both a transmitter and a receiver. I use these, and they work fine. Working with wireless means you can move anywhere within range of the receiver to fire the flash.
Multiple flash units off camera
Once you have established a wired or wireless connection to one flash, you can add multiple flash units in a couple of ways. For wired, you can continue connecting a synch cord from flash to flash. For wireless, each new flash requires a new receiver.
Another alternative is to add flash units with built-in flash-sensitive remotes. A flash with a built-in remote sensor will fire when it detects the light of another flash.
In this scenario, your camera-mounted transmitter fires your first flash, which in turn triggers the other flashes with their built-in sensors. The disadvantage in this setup is that anyone else using a flash will fire your units with the built-in flash sensors.
If you already have extra flashes but without built-in remotes, you can get fairly inexpensive add-on remote sensors to attach to the flash. A good source for exploring this option is at FlashZebra.com.