Der sicherste Weg, einen jungen Menschen zu korrumpieren, ist, ihn zu lehren, die, die gleich denken höher einzuschätzen als die, die anders denken.
This sentence is like an onion: layers upon layers. The easiest way to deal with such sentences is to peel them apart bit for bit. First, the main sentence:
Der sicherste Weg ist, ihn zu lehren.
The most fool-proof way is to teach him.
The next layer is the answer to the question the most fool-proof way - to do what? The answer is a relative sentence:
einen jungen Menschen zu korrumpieren
Der sicherste Weg, einen jungen Menschen zu korrumpieren, ist, ihn zu lehren.
The most fool-proof way to corrupt a young person is to teach him.
Now, this begs a question: to teach him - what? The answer to this is another relative sentence:
die höher einzuschätzen als die
The first "die" hier means "the [ones]" and the second one "the [others]". If you ask now who or what the ones and the others are: we will come to that.
Der sicherste Weg, einen jungen Menschen zu korrumpieren, ist, ihn zu lehren, die höher einzuschätzen als die.
The most fool-proof way to corrupt a young person is to teach him to hold the [ones] in higher esteem than the [others].
Finally, we need to adress who the ones and the others are. This is explained in two other relative clauses, following the respective "die":
die, die gleich denken
die, die anders denken
So, the first "die" are "the ones thinking the same" and the second "die" are "the ones thinking differently". In English one would always use "the ones - the others" and in German that is possible too, but not necessarily so. In German it is possible to define what is meant in a relative clause and have the respective Demonstrativpronomen1) - here "die", because it is Akkusativ Plural in the sentence higher up in the hierarchy stand in for the rest of the clause. For instance:
Das, was man nicht selbst produzieren kann, muß man kaufen.
[That] what one can't produce himself, one has to buy. - One has to buy what he cannot produce himself.
The main sentence is "Das muß man kaufen." (One has to buy that.) and what "Das/That" exactly constitutes is explained in the clause following the Demonstrativpronomen: "was man nicht selbst produzieren kann".
Now, here is the whole sentence again:
Der sicherste Weg, einen jungen Menschen zu korrumpieren, ist, ihn zu lehren, die, die gleich denken höher einzuschätzen als die, die anders denken.
The most fool-proof way to corrupt a young person is to teach him to hold the ones who think the same [way] in higher esteem than the others who think differently.
1) Notice that "die" is NOT an article here, although it looks like and is inflected like one.