I have a Sony NEX6 and a couple Nikon speedlights. What do I need to have the NEX6 trigger the Nikon wirelessly?
If your speedlights have flash synch cable receivers you can use any wireless trigger combination. If they don't you can buy hotshoe adapters with a flash synch reciever and do the same.
Personally I use pocket wizards exclusively (plus III), love them. The first trigger would go in your camera's hot shoe. The second you would plug in via cable to the flash. You will need a 1/8 to PC cable (these are usually included).
If your Nikon speedlights have SU-4 mode in them (the SB-600 doesn't), you could use SU-4 mode on the speedlights, and the pop-up flash on the NEX6 in manual mode to trigger the lights.
If you get manual radio triggers that are transceiver units (i.e., can be used as either a transmitter (Tx) or receiver (Tx)), it must have some way of switching between Tx/Rx modes. Or you need to get separate dedicated Tx/Rx units (this is why the Cactus V, RF-602, and RF-603 II triggers work on NEX/Fuji X/micro four-thirds, but the RF-603 triggers won't). The Rx/Tx switching on the RF-603 is done using a TTL signal that doesn't occur on the same pin (or at all) on the mirrorless hotshoes, as it does on Canon/Nikon hotshoes.
You mention in a comment on Robert Lowdon's answer that you're using a Nikon SB800 speedlight. There are plenty of wireless triggers you can use and the PC sync, as noted, however there's another (completely free and easy) option built into the SB800: the optical slave trigger. Enable this mode and when the flash sees another flash go off (such as your NEX 6's built-in flash), the SB800 will go off.
The trouble with the optical slave is that it relies upon line-of-sight communication and often won't work in very bright conditions.