Hm. That's unfortunate... And I've just checked on Duolingo, and I guess it also doesn't explain these points anywhere close to the start... I mean, I can try to explan, although I have to say that my, if not theoretical, then practical grasp on adjective declensions is shaky at best.

Also, you shouldn't have capitalized "schnell" when copying. It's an adverb, doesn't require capitalization.

Anyway, in the order of appearance:

anziehen is a compound verb which consists of the root "ziehen" ("to pull") and the prefix "an", which is in the category of separable prefixes. This means that in certain cases they part ways with the root, to usually take place at the very end of the sentence. In a fashion, they're a hint of the quite regular phenomenon in English - phrasal verbs, such as "give up", except... well, they're very different. But I think, also similar. So you could try to translate "anziehen" as "to onpull", and then that sentence should make a little bit more sense.

neuen and schwarzen are part of the same problem - adjectives in German also require declension, and the way they do it depends on a lot of factors, among them the presence and type of article and gender and number of the noun (if any). In your sentence, for example, neu and schwarz follow "meine" (plural for "mein") and precede a plural noun - Socken. "Mein" is kind of in the same category as the indefinite article, as far as what it does to adjectives... which is, well, adding "en" to adjectives before plural nouns. I'm pretty sure it doesn't depend on the case (if you're wondering, Socken are also technically an accusative object, although it doesn't do anything to it).

Yeah, that's pretty complicated. Don't know if you can understand what I tried to explain, on rereading it seems pretty dense.