Superglue but should be the Gel type. The liquid type runs across the hardscape and once wet shows up. With the Gel type dab a spot on several parts of the underside of the plant rhizome and then hold against the hardscape item for several minutes.
For wet wood yes, I lower the water level to an inch or 2 (making sure all the fish are in that water and saving enough water to make up 50% tank volume, then put a blob on the hardscape and then hold plant to it as above.
For mosses I roll them into little '3mm' balls and the same, push onto blob of gel.
Then I spray the whole lot and leave it for half an hour (to make sure it cures)
Once done return water level to 50% and fill to top with fresh water.
I don't do moss stones. I do single pieces of gravel and again push the 2-3mm ball of moss/fissidens onto it, then I can drop these into the substrate whenever and wherever I want
Oh and I would easy win the speed attaching contest although I tend to do it slowly anyway. I like to do things carefully but it really is a case of dab, push hold ready.
Used to use hairnets for Riccia but stopped because spiny fish (Otos, Corys, Plecos) kept getting hooked on it. Used to use cotton thread but as stated above the parts that bridge gaps would damage or trap fish. Never used fishing line for the same reason as cotton wool.
Used to use elastic bands as above. Not sure how they use elasticity before the plants attached. Normally about 4-6 months and then they can be removed pretty easily when they have deteriorated. Anubias and Ferns usually attach within a month or 2, Ferns more often than not quicker.
Use cable ties rarely but only if I'm being lazy or the tank is not on show. If it is a tank that isn't in a cupboard I won't use cable ties. I prefer to use something I can do and leave, not have to dig in and remove at a later date.
Andy