You need three RF-603II units: one on the camera to act as trasmitter, and one on each flash to act as receivers. The YN-568EXII does not have any built-in radio slave capability. All its slave modes are optical, and to be used with the RF-603IIs, a flash must be out of all the slave modes (because they tell the flash to listen only to the optical sensor, not the foot. And the radio trigger talks to the flash through its foot).
The RF-603II triggers are manual-only, so you will only be able to tell the flashes to fire. You won't have remote power setting control, eTTL, or HSS. The flashes must be in M mode, and you'll have to dial the power setting in on the flashes themselves.
A few other things to check:
All batteries are in good health and fully recharged.
That all the triggers are using the same channel. You set the channels via the dip switches in the battery compartment.
That your transmitter unit is full seated on the camera hotshoe
If you're moving up from YN-560 units, and you want TTL/HSS, your best bet is to go with the YN-622 triggers (two YN-622Cs for the flashes and a YN-622C-TX for the camera), or return your YN-568EXIIs, and wait for the YN-685EX to come out (which will have a built-in 603/5+622 receiver in it). Otherwise you might do better to simply use YN-560III/IV units with a YN-560-TX transmitter--you'd at least get remote power control, which the RF-603IIs on YN-568EXIIs don't.