Having installed the saddle and piercing valve am I supposed to open the valve

Did you close the valve all the way and pierce the pipe? If so, open the valve. Saddle valves are not approved by many local codes as they are prone to leakage as they age.

Yes, now you open the valve if the other end is connected to what you are adding.

I always remove the valve after piercing the copper line and drill an 1/8" hole where the line was pierced and deburr the hole with a pocket knife and light sandpaper in order to allow enough water to pass. When you re-install the saddle valve turn the valve clockwise almost all the way out so you center the needle in the hole, then tighten the screws equally, but before fully tightening the screws loosen the needle valve to avoid pushing the needle too far in the hole. You should be able to control the water flow after it's fully tightened down. They make several other ways to add another water valve and line that work much better than a piercing valve. Sometimes you will not have enough water flow to get an ice maker to work correctly, but if you use a tee to install the new line the water flow is much better.