I'm shooting a D7100 and I have two flashes: an SB-700 and a Yongnuo 560 II. I have two Yongnuo RF-603 wireless triggers.
How do I fire these two flashes?
Do I need to buy two more triggers or is there a way that the SB-700 can communicate with the triggers?
To use these two flashes off camera with RF-603 triggers, you need three RF-603 units: one to act as the on-camera transmitter, and two to act as receivers on the feet of the flash units.
You do need to understand that the RF-603 triggers are manual-only, and that you will not be able to use iTTL, or FP/HSS, that your remote flashes have to be used in M mode, and that you'll have to explicitly set the power levels on the flashes themselves.
To use the units:
Check that all the triggers are set to the same channel (the channel is set with DIP switches in the battery compartment).
Check that all your batteries (both for the flashes and triggers) are fully charged and in good health.
If you have RF-603, not RF-603 II, units turn on the receiver units (because the on/off switch is placed exactly where you can't reach it once you put a flash on top of it), and attach to the flashes. Otherwise, attach, turn on the flash, and then turn on the trigger.
Put the flashes in M mode.
Place the transmitter unit on top of the camera, making sure it's seated fully forward in the shoe--mis-seated units are the most common cause of misfires or non-firing.
Turn on the camera, and then turn on the transmitter.
You should now be able to fire the flashes when you press the shutter button or the test button on the on-camera transmitter.
You also don't need to use the RF-603s to trigger one or more of your flashes remotely. You could also use optical slaving where a "master" light pulse(s) from the camera's pop-up flash can trigger the remote flashes. These optical modes may have difficulties in bright light and outdoors, or without "line of sight" where the flash's sensor can't "see" the master flash burst. In those cases, radio triggers are a better bet.
Nikon's Creative Lighting System (CLS) lets you fire your SB-700 off-camera with iTTL and FP/HSS capability, by putting the D7100's pop-up flash into commander mode and the SB-700 into CLS slave mode. But this won't fire the YN-560II (you'd need a Yongnuo flash with "EX" in its name).
If you need to fire both of your flashes, they also both come equipped with "dumb" optical triggers. Unlike CLS, the only signal that can be communicated is the "fire"/sync signal, so this, like using the RF-603s, is manual-only triggering. So there is no iTTL and no FP/HSS.
Put the YN-560II into S1 mode; put the SB-700 into SU-4 mode, make sure that the sensor panel on the side of the SB-700 and the red sensor panel on the front of the YN-560II both point at your camera, and then put the D7100's pop-up flash into M mode (and out of commander mode), and when the pop-up flash fires the remote flashes should fire.
