The last part of your basic kit you will need is a way to trigger the flash to fire when you click the shutter on your camera.
PC Cord
If your camera and flash both have a PC port, then this is the cheapest, most reliable method to triggering your flash. If your camera lacks a PC Port you will need this adapter, if your flash lacks it, get this adapter. You will also need a PC cord to connect the two ports.

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Optical Triggering
Some flash systems like Nikon's CLS allow TTL wireless triggering using the popup flash to tell your remote flashes when to fire. This is only available on the Nikon D90 and higher models (D300/D300s/D700) and Canon 7D. If you have one of these cameras and the same brand flash as previously recommended, you are ready to start playing with light!
Both Canon and Nikon sell infrared TTL transmitters that work in the same way, requiring line of sight of the flashes. Nikon's is the SU-800 (not necessary on D90 and higher cameras with a flash) and Canon's is the ST-E2.
Wireless Triggering
Wireless triggers are the fanciest and most expensive method of triggering your flash. They are also the most convenient and reliable method (but at a price). There are many different wireless triggers, but the ones that work the best are the commercial grade PocketWizards and the more budget friendly RadioPoppers and AlienBees Cybersyncs. A set of these can easily set you back several hundred dollars. There are cheaper variants for less than $50, but they can be quite unreliable and have poor range.
And that is all you will need to get started in off-camera flash! The only thing that will hold you back now will be your creativity and the urge to get more lights and stands. If you want to learn more, check out Strobist, the go-to resource for all things off-camera flash.