This is covered in section 1.5.5.
First, on the ship log, the "CA (CL)" means your ship has CA hull armor, and CL armor on the main battery turrets. The hull armor also nominally identifies what classification your ship is WRT things like Equivalent Damage Rolls (EDRs), Collisions, etc.
Now, on the Gunfire CRT (GCRT), assume a USN ship is shooting 9x 8" guns (3x triple turrets) at that ship from an actual range of 16,000 yards during the daytime: On the USN GCRT, cross referencing the 16,000 yard actual range - moving up to the 18,000 yard row - and 8" guns gives you "1+ CL". You need to note that "CL", as that is the actual penetration - i.e. regardless of any row shifts to hit. Let's say the culmination of row shifts results in going down one row; you're now on the 15,000 yard row, which reads "1+ CA". The ship is still hitting on "1+" - i.e. a 1 or a 10 on each D12 (and you'll be rolling 4 D12s for 9x guns, 1 per 2 rounding down for triple turrets). Say you roll the 4 dice and get 2 hits.
You now look down on the EDR table, and cross reference the CA target classification with 8" guns, and see it reads "x1 1/2". Multiply the 2 hits x 1 1/2 means the target has taken 3 EDRs - i.e. the target player will roll 3 times on his Gunfire Damage Table. If you only had done 1 hit, 1 x 1 1/2 is 1 1/2. For 1/2 results, roll another die, ODD = a hit.
When the target player does his damage rolls, he needs to be cognizant that since those 8" hits only penetrate "CL", if he rolls main battery damage, the shots penetrate and do full damage. If the hit is on the hull, they do half damage, and if the hit is on something else inside the thick black lines for the hull (e.g. Engineering), it does not penetrate and is no effect.
Night is a little more complicated, but the concept is the same. You need to use the actual range on the daytime range scale to note the penetration, but use the night range scale, with row shifts, to determine the to hit numbers.