Some ingredients do not dissolve well in hot water - the starch swells and thickens, forming lumps that may have raw powder in them and are nasty. They need to be added to cold or lukewarm water and heated after they are dissolved. Other ingredients, most notably pasta, will partially dissolve in cold water making a thick gloppy soup. But if you add them to hot water they will "seal" (in a way) and stay together as they cook.
This a a great video that explains every step. She cuts the head off by slicing above the eyes, so removing the beak is a part of cleaning the tentacles.
These are your first cuts.
Cut the head off above the eyes, and slit the head open. Rinse out the guts, there will be some connective tissue that needs to be cut away or broken to get to all of the yucky stuff. Rinse thoroughly and peel. It's easy.
Cut the tentacles away below the eyes (the slice now that contains the eyes can just be tossed). That will expose the beak, which is at the center, where the tentacles meet. That just pops out.
The tentacles can just be rinsed and cut as desired.
Easy, and totally worth it. Good luck.
Of course you can keep the octopus "whole" by slicing out the eyes in a kind of pie wedge shape cut, exposing the beak and guts to be cleaned away but keeping the connection between the tentacles and head intact at the "back", otherwise following the instructions in the video.
Best Answer
The muscle fibers of octopus are very thin compared to other species, arranged in multiple layers and alternating rings, which are then even further reinforced with collagen, 3-5 times more than regular fish muscle fiber. It's basically the reinforced concrete in the world of muscle fibers.
There are exactly two ways to get tender octopus:
Note that these two methods generate edible octopus, but with different texture.
The wine cork serves no purpose. If it has any effect at all, it will negatively affect the destruction of the collagen, as tannin is actually used to cross-link, a process to make the collagen stable and durable, which is the complete opposite of what you want, when you want tender octopus.
References:
[1]: On Food and Cooking
[2]: Stabilization of Collagen by Its Interaction with Tannin
[3]: Tannin used for the conservation of leather by stabilizing collagen
As an unrelated side note, octopus and squids have the least flavorful flesh of all fish and molluscs, as they use Trimethylamine N-oxide for osmotic balance; which happens to be completely tasteless. Other species use tasty amino acids. Unless you happen to have one as free by-catch on your own fisherboat, there is not much reason to invest the time and costs to make a dish out of it.