What is the difference between sit/set and lie/lay?
These two pairs of words operate on the same rule, a rule that has to do with transitivity. Transitivity is a property of verbs that allows them to take direct object, a second noun directly after the verb without an intervening preposition. In the sentence, "Frank bit the dog," "Frank" is the Subject (doer) of the sentence. "Dog" is the object ('doee'), the object to which something is done. "Bite" is a transitive verb in that it allows a direct object (the bitten dog above). Other verbs, like "sleep," do not allow direct objects. You can't say "Frank slept a dog." You can say "Frank slept all night" but "all night" is not the object to which something is done but an adverbial phrase telling us how long the action of the verb lasted.
That brings us to sit/sat and lie/lay. "Sit (sat, sat)" and "lie (lay, lain)" are intransitive verbs. You can sit down, sit up (movement involved), or sit in a chair (no movement) but you can't sit Frank-or anything else. You can, however, set a plate on a table or seat Frank in a chair-but not sit him. "Set (set, set)" is a transitive verb; "sit" is intransitive. This same distinction separates "lie" from "lay (laid, laid)." You can lie on a rug but you cannot lie a rug. You can, however lay a rug anywhere you please or lay down your troubles with lie/lay if you understand this brief note. The confusion here arises from the fact that the past tense of "lie" is also "lay." Don't let that confuse you.