Golpalott's Third Law is stated in full by Hermione in Harry Potter and the Half-Blood Prince (HBP):
'Settle down, settle down, please! Quickly, now, lots of work to get through this afternoon! Golpalott's Third Law ... who can tell me -? But Miss Granger can, of course!'
Hermione recited at top speed: 'Golpalott's-Third-Law-states-that-the-antidote-for-a-blended-poison-will-be-equal-to-more-than-the-sum-of-the-antidotes-for-each-of-the-separate-components.'
Harry Potter and the Half-Blood Prince - p.351 - Bloomsbury - chapter 18, Birthday Surprises
There's no indication at all that there's any more to it than that - and every indication that that's all there is.
Slughorn immediately replies to this:
'Precisely!' beamed Slughorn. 'Ten points for Gryffindor!'
Harry Potter and the Half-Blood Prince - p.351 - Bloomsbury - chapter 18, Birthday Surprises
And then later we have:
Harry pulled out his trusty copy of Advanced Potion-Making and turned to the chapter on Antidotes. There was Golpalott's Third Law, stated word for word as Hermione had recited it, but not a single illuminating note in the Prince's hand to explain what it meant.
Harry Potter and the Half-Blood Prince - p.352 - Bloomsbury - chapter 18, Birthday Surprises
Now, after Hermione has quoted the law, Slughorn goes on to add:
'... which means, of course, that assuming we have achieved correct identification of the potion's ingredients by Scarpin's Revelaspell, our primary aim is not the relatively simple one of selecting antidotes to those ingredients in and of themselves, but to find that added component which will, by an almost alchemical process, transform these disparate elements-'
Harry Potter and the Half-Blood Prince - pp.351-2 - Bloomsbury - chapter 18, Birthday Surprises
The quote is cut off there.
So the premise of your question is absolutely right. It is merely a generic - though I hope you'd agree deep and important - law of potion-making. It tells you that it is insufficient to merely identify the components of a blended poison (one made by mixing multiple poisons) and mix together the antidotes of each poison. No you must "find that added component which will, by an almost alchemical process" complete an antidote to the blended poison as a whole - the blended poison being a new, different entity - more than the sum of its parts. Thus, its antidote must be the same.
It most certainly does not specify how to obtain the necessary ingredients. In fact, that seems to be the whole point of the lesson. Scarpin's Revelaspell will identify the ingredients of the blended poison and then, presumably, there is a list or reference work which you can consult to find the antidotes to each of these poisons. But to create an antidote to the blended poison, you must have insight and skill and knowledge. You must be able to work out what you need to add.
What this of course means is that the task of finding an antidote to a blended poison is very difficult, and you would certainly have to be very capable to be able to do it. You'd also have to understand potion-making. It's not just a case of following instructions from the blackboard, or a book, like most Potions lessons:
'It's a shame that the Prince won't be able to help you much with this, Harry,' [Hermione] said brightly as she straightened up. 'You have to understand the principles involved this time. No short cuts or cheats!'
Harry Potter and the Half-Blood Prince - p.352 - Bloomsbury - chapter 18, Birthday Surprises
We see later in the chapter:
Hermione, who was sweaty-faced and had soot on her nose, looked livid. Her half-finished antidote, comprising fifty-two ingredients including a chunk of her own hair, bubbled sluggishly behind Slughorn, who had eyes for nobody but Harry.
Harry Potter and the Half-Blood Prince - pp.354-5 - Bloomsbury - chapter 18, Birthday Surprises
However, you seem also to be asking whether Harry really had difficulty understanding the law. Sure, he might have failed the task, like Hermione and everyone else - but surely he understood the Law, even if he couldn't concoct an antidote?
Well, in the books, he does indeed fail to understand the law, just as the Wikia article says:
After Slughorn exclaims "'Precisely!'" and awards Gryffindor the points, we get:
'Now, if we accept Golpalott's Third Law as true ...'
Harry was going to have to take Slughorn's word for it that Golpalott's Third Law was true, because he had not understood any of it. Nobody apart from Hermione seemed to be following what Slughorn said next, either.
Harry Potter and the Half-Blood Prince - p.351 - Bloomsbury - chapter 18, Birthday Surprises
(What he said next was the bit about Scarpin's Revelaspell and finding that added component).
So, how, you seem to be asking, could he have failed to understand it? Well, in fairness to him, Hermione did recite it at top speed, so I'm not surprised he didn't take it in first time. But then, as I quoted above, he looked at the textbook and there it was, in black and white, in front of him. He had plenty of time to read and absorb it.
Out-of-universe: Rowling's writing for a young-ish audience that may be fairly impressed by the technical-sounding language.
In-universe: Well, I guess Harry's not as smart as you, Hermione, or the Prince.
To be fair, this kind of thing is quite a long way from what we usually see of Hogwarts lessons - very theoretical and technical. Our usual glimpses of Hogwarts life - and particularly Potions classes - is more hands-on and less scientific. Maybe he's just not used to this kind of thing? And nobody ever said Harry was an academic sort of a chap.
Well, it's a thought. On the other hand, it is stated and implied in numerous places that Hogwarts lessons feature theory heavily, as well. For example, OWL exams have a theory component, in numerous places there are references to students taking complicated notes (e.g. in the first ever Transfiguration lesson in book 1 (The Potions Master), the homework essays are generally quite theoretical, etc. etc.
I don't think I can supply you with a more satisfying and complete in-universe answer than: he just didn't get it. Because in the books, he really didn't get it. For once, the Wikia article seems to be on the money.
