First off, please be sure to get the Nikon version of the YN568EX III. It will have the YN568EX III name displayed in gold lettering. The Canon version has silver lettering.
If you want to use radio wireless (you probably do)
To fully control the flash you need a YN622N radio set. A YN622N-TX transmitter or YN622N / YN622N II transceiver (combined transmitter & receiver) can be used on the Nikon camera's hot shoe. A YN622N / YN622N II can be used as the receiver attached to the flash's hot foot. The advantage of the YN622N-TX transmitter is the LCD display and additional control buttons that make it much easier to see how you have your flash(es) set and to change the settings of your flash(es). The YN622N or YN622N II can be used, but the controls are a bit less intuitive and you'll have to count how many times you click certain buttons. The YN622N-TX transmitter and YN622N/YN6222N II transceivers are about $40 each. You can buy YN622N-TX + YN622N II sets, or sets of two YN622N II transceivers for around $80.
If you want to use optical wireless (you probably do not)
You need any Nikon iTTL capable "master" flash or controller attached to the camera's hot shoe. Some of those are: Nikon Commander SU-800, Nikon SB-910, SB-900, SB-800, SB-700, and any third party clones. You also could use a Nikon body with a built-in flash that is capable of being a "Flash Commander". Some Nikon cameras have popup flashes that are Commanders, others have popup flashes that are not Commanders.
Disadvantages of optical wireless vs. radio wireless
There are disadvantages with using optical wireless communications instead of radio communications, though:
- Distance limitations. Most optical systems, especially when using a weak built-in popup flash as the controller, are much more range limited than radio systems.
- Positioning limitations. Most of the optical controllers only cover an area about as wide as a 24mm lens on a FF camera. If the remote flash is further to the right or left it may not receive any optical signal, even if it is only a few feet from the camera! Radios transmit in all directions from the camera.
- Line-of-sight requirements. In addition to being in the "cone" of light transmitted by the master, off camera flashes must have a clear line-of-sight to the master with the optical receiver on the flash pointed in the direction of the master. This inhibits being able to place optically controlled flashes inside modifiers, placing them behind objects in the scene, etc. Radio systems are not limited to line-of-sight and can even be used on the other side of walls and other obstructions (although the obstructions may reduce the range somewhat).
- Difficulty with bright ambient light. Especially outside under sunlight, the power of optical wireless control is very limited. Again, especially with a relatively weak built-in popup flash, the master just doesn't have much power to cut through the bright sunlight and the receivers can't detect the weak signal from the master over the very bright sunlight. Radios work just as well in bright sunlight as they do in a dark studio.
About the only advantage optical control has over radio control is that you don't need an on-camera radio transmitter attached to your camera's hot shoe if your camera has a built in flash that can be used as a Commander/Master to control off camera flashes. Some cameras with popup flashes have that ability, other do not. (But you'll probably soon discover that you'll need a more powerful on-camera optical master attached to your camera's hot shoe to get the optical system to work the way you want, if it will even work then.)
For these reasons, most systems have moved on to radio control of off camera flashes.
You might also consider the Yongnuo YN685N. It's basically the same flash as the YN568 II, but it has a built in radio receiver that can work with a YN622N transmitter, as well as in manual only mode with YN560/RF605/RF603 transmitters. It does not have optical wireless capability like the YN568EX II does.
The YN685N costs about $25-30 more than the YN568 II, but you don't need to buy a $40 radio receiver for it. You would still need a transmitter on the camera's hot shoe. For full iTTL capability, you'd need a YN622N-TX or YN622N II. For manual only capability you could use a YN560-TX, RF-605, or RF-603 transmitter that controls Yongnuo's manual only flashes such as the YN560 series. (Note that while a YN560/RF605/RF603 transmitter can control a YN685N flash manually, a YN622N transmitter can not control YN560 series flashes.)