I have a Canon 60D and a Speedlite 430EX II. Does anyone know if I can fire the speedlite remotely without firing the built in flash as well? So far I have only been able to fire them both.
The 430EXII supports Canon's now older method of remote flash triggering, which uses flash pulses from the commanding unit to trigger the remote unit (430EX in this case). The newer system, based on radio, is supported by the 600EX-RT, and ST-E3-RT units.
Your system uses flash pulses, which fire BEFORE the shutter opens. So, even though you are seeing the flash on your 60D fire, it isn't necessarily contributing to lighting the scene, depending on how you have things configured.
The newer 600EX-RT system does not use flash pulses, so this problem does not exist. It can, and is supported by camera models that do not have a built-in flash, such as the 5DMkIII and 1DX.
No, the pop-up flash on your camera has to fire to be a wireless master for the off-camera 430EXII. The camera body and the flash communicate with light pulses ("pre-flashes"), so there will always be some firing of visible light pulses from the master. You can set the pop-up flash not to contribute light to the image. But light pulses are needed to set the remote flash's power, to perform any metering preflashes for eTTL, and, of course, to communicate the sync signal itself.
There's a little argument about whether or not the pop-up flash in master mode will fire during the exposure--some people say you can see it at macro distances or in mirror-selfie shots. But for normal subject distances, whatever light is coming from the master is low enough not to register in the image. With Nikon, the commander definitely fires during the exposure, even when set to "--" (don't contribute); again, it won't register at normal subject distances, but Nikon also sells an IR filter to put over the pop-up flash if it becomes an issue.
However, there are limitations inherent in any optical triggering system. Typically this type of system works better indoors in lower light conditions. The red sensor panel on the front of the flash (or side if you shoot Nikon) must be able to "see" the mastering light pulse. Indoors, with bounce surfaces, this requirement isn't particularly stringent. And in lower light, the mastering signal will register clearly. However, outdoors in bright sunlight, the story changes and range and reliability tend to decrease. This is why radio triggering is so popular, and why Canon built it into the 600EX-RT and ST-E3-RT.
There are a wide variety of radio triggers these days that cover all kinds of functionality and price ranges--you don't have to get a 600EX-RT to wirelessly trigger a Canon flash over radio. Just keep in mind that you can typically only have two of the following three things with radio triggers: low cost, a lot of features, and reliability. :)
I don't have the 60D, but I had a T4i which also has a built in flash like the 60D. Yes, you are able to use the built-in flash to trigger an off-camera flash while NOT having the built-in flash contribute to the scene. You need to look in the camera flash settings - not the off-camera flash unit. There is a setting there where you can choose to have the built-in flash to contribute, or alternatively, have it NOT contribute.
One thing I did while doing some off-camera flash work before I had the radio transcievers was to use optical triggering, but with a very low flash power relative to the flash power of the output units. It could possibly be a little unreliable, but optical triggering tends to be unreliable anyway, hence the recommendations for radio triggering systems.
Actually, you can buy radio transceiver pairs fairly cheaply - one sits on the bottom of the external flash, and one in your hotshoe. You lose all E-TTL functionality, but you lost that anyway when you took your 430EX-II off-camera.
I should also point out that generally, the bridge flash of such cameras are not so high output compared to dedicated speedlites. So even if your speedlite is at 1/16 and your bridge is at 1/16, there's probably already 2-3 stops difference (varying with the distance of the camera from the subject with respect to the distance of the flash to the subject).