What size hole needs to be drilled into the door for the SK910 handle set?

Check out the SK910 product page, be sure to read the instructions under "Support" tab.

You need to pre-drill three holes through the door. Each should be 5/16" in diameter.

The distance from the top hole center to the bottom hole center should be 1.75", with a third hole in the middle. 

You also need to drill a fourth hole at the bottom of the handle, but it doesn't need to be pre-drilled. You can do that after installing the handle & the latch and when everything functions well. This will help ensure the fourth hole lines up properly.