How do I connect a single pole light switch with three 2-wire cables in box?
If you are sure that there is only 1 (one) always hot black wire, then follow these steps:


Turn off power at the breaker.
Connect all of the ground wires together with a wirenut and stuff them in to the box.
Connect all of the white wires together with a wirenut and stuff them in to the box.
Get yourself a 6 inch piece of black wire and strip the ends. You've just made yourself a pigtail. Match the gauge of this wire (12 or 14) to the gauge of the wire already in the box. Connect one end to the switch.
Connect the other end of the pigtail to the always hot black wire and one of the other black wires with a wirenut.
Connect the remaining black wire to the switch.
Install the switch and cover.
Turn on the breaker.
Turn the switch on and off. If it controls the light, you are done.
If the switch doesn't control the light, turn the breaker off and repeat from step 5 but swap the two black wires that are not always hot.