We just learn them growing up. Chinese has a lot of close synonyms too, but you don't have to look them up, do you? For example, 带 and 穿 can, in the context of clothes, seem like synonyms to English speakers; but there is a definite difference to native Chinese speakers. Similarly, native English speakers instinctively know the difference between "study" and "learn". In both English and Chinese native speakers might need to look up words if they're very rare or formal, and in both languages there are cases where even native speakers use words incorrectly; but most of the time native speakers learn the differences as children between close synonyms without studying (see what I did there?).

If you're talking about that specific example, studying is opening up a book and reading or filling your brain with relatable content to understand something better, whereas learning is what's going into your brain and what you're being taught. If you're talking about finding synonyms in general, I suggest a thesaurus or just finding the answers online. Hope this helped:)