Yea, either your PSU will have the 6-Pin Connector and you can go straight from the PSU to the card, or you can use the adapters packaged with the card and plug the adapter into the Video card and the other end into the applicable connector coming off the PSU.
Correct ! - THe one that comes with the video card is a molex (power connector that is also used by your Ide devices etc.) on one end and a 6-pin power plug on the other that goes into your video card - if your PSU already has a 6 pin you will not need to use the cable that comes with the video card. Also with the 5770 you will get a Xfire connector which you will not use unless you are using 2 video cards and a DVI to VGA adapter that you willl not use unless your monitor does not have a DVI connector. - so most of the hardware will not be used unless you have some older hardware that requires the adapters !