As I understand one can make kosher any kli sheni [spoon,knives etc] by just pouring boiling water over it form a kli rishon [and certainly by hagala]
I also understood that a big spoon one can be kashered by first dipping one part of it in a boiling kli rishon and then dipping the “second”part [or by pouring boiling water over various the parts from a kli rishon].
Can one use any kli rishon one has at home [being meaty or dairy, after it has not been used for 24 hours] for this process of koshering or does one has to kosher the pot itself first by letting boiling water cook over its brim?
Pesach kasher ve sameach
After it has not been used for 24 hours it may be used for hagala kashering. This is true of meat and milk. WIth regards to kashering for Pesach, while the above is also true [using a chametz vessel], the widespread custom is only to kasher in a pot which is kosher for Pesach.
Your initial statement is correct, however a spoon and knife is not always a kli sheni. If it became non kosher by cutting food in a pan from the oven or stirring a soup on the fire, i.e. from a kli rishon, they may not kashered with pouring from a kli rishon, only by immersing in a kli rishon itself.
See Shulchan Aruch O:C 452:2, MAgen Avraham ibid. 6, Taz 10, Mishna Berura 13.