I use this: http://amzn.com/B002W3IXZW from cowboy studio or if you have more money I would get this: http://amzn.com/B00BBQ8IDS from Pocketwizard which was just released. Many people also praise the inexpensive Yongnuo transmitter/triggers.

The 60D even has a built in wireless transmitter. The 60D's built-in flash can act as a controller or commander to multiple, remote wireless flashes. It is a pretty great feature first introduced in the 7D. As far as I can tell, the 430EX will work in slave mode with the 60D in this way. I haven't looked too far into it though to confirm.

You can optically trigger with the 60D since it has a built in flash, without any additional equipment. It just isn't all that reliable and requires line of sight.

The 6D does not have a built in transmitter unfortunately, or a flash, so you need to either buy a 580ex/600ex style flash or a flash trigger like I linked to above.

In essence, if you are looking to use one system with both flashes, you will need to invest in some new equipment.

Finally, I would highly recommend buying this book if you are new to flash on the Canon system: Mastering Canon EOS Flash Photography by NK Guy http://amzn.com/B004J4VVN8 A great deal of it is also available here for free: http://www.photonotes.org/articles/eos-flash/