At this point, how you remove the cork from the wine bottle becomes a matter of experience.
If you haven’t frequently opened wine bottles with a corkscrew while holding the bottle in one hand and the corkscrew in the other, it can be awkward and appear to guests that you are unprofessional.
In this case, the best way to open the bottle is to place the bottle upright on a side table (preferably) or the diner’s table and hold the bottleneck from moving with one hand and press down on the corkscrew and start turning it with the other hand.
It is best if you twist the corkscrew almost all the way through the cork to avoid breaking the cork when you pull, but try to avoid going too far through so you don’t carry bits of cork into the wine which is unsightly for the guest. Those cork bits may need to be removed from the wine in the glass and discarded, but ask the guest if they would like a new glass and wine pour rather than using a spoon to remove bits from their glass.