Compression ratio is: volume at bottom-dead-center divided by volume at top-dead-center.
Essentially, you'll need to know your bore size, stroke length, distance from top of piston to bottom of head at top-dead-center, and head combustion chamber size.
That's sounds difficult to do, but it's pretty simple. A standard Chevy small block 350 has a bore size of 4.00 inches and a stroke of 3.48 inches. This computes to a single-cylinder volume of 716.62 cubic centimeters. Now, for the total combustion chamber size (volume at top dead center), you need to add the head cc's to the volume between the top of the piston and the bottom of the head at top-dead-center. This is a combination of top-of-piston to top-of-cylinder height at TDC and head gasket thickness. For the purpose of carrying out these calculations, let's call that distance 0.030 inches.
If I remember correctly, the combustion chamber size of a vortec head is 68 cubic centimeters (might be 72...I'm drawing a blank right now). Adding in the volume stated above, we get a total combustion chamber size of 74.17 cc's.
So, volume at bottom-dead-center divided by volume at top-dead-center = 716.62/74.17 = 9.66.
These are all general calculations and will vary based on your head size, whether or not you've bored out your cylinders, and how much clearance you have from the top of the piston to the bottom of the head at TDC.