So ligger means that something is already on (no action) , but lägger is the action of putting?
Yes, that is right. The same difference goes for sitta/sätta, stå/ställa as well.
wait, what is the difference between ställer and lägger, is lägger more lay?
Ställa is to put something in an upright position, lägga is to put something in a lying position. Thus both ställa boken på bordet and lägga boken på bordet are correct translations of put the book on the table, but they mean slightly different things in Swedish.
"Duk" can, however, mean "cover" in certain contexts. The factory in which i work calls the covers on our rollers "duk"
I'm no Native Speaker and I wonder why it isn't "onto the table". Is it because of the "put"?
It's kind of hard to distinguish the usage, for the most part "onto" is used when there's direction involved and "on" usually implies stationary location, but that's not entirely accurate. Sometimes they are interchangeable. However, for some reason it feels more natural to say "put something on the table" rather than "onto" even though there is some sense of the object moving from one location to the other.
This happens with a lot of instances of "put": "I put a new leash on my dog." "He put a bandage on the wound." "I put my left foot on the ground."
So you are probably right that "put X on Y" is idiomatic English.
My sambo says 'dukar bordet'. Is there a difference there? Does 'dukar bordet' mean set the table, with plates and everything?
Yes. A table with a cloth, "duk", and no more, is not considered "dukat". You must prepare it to be ready for eating.