Basically, delving into culture which contains common phrases, idioms and sayings scattered around. You hear/read them, understand meaning from context, and commit to memory so you can use it later on.
This is not really that different from how kids learn idioms too, isn't it?
By the way, a lot of idioms/saying are pretty similar in different countries. Their wording might be slightly off, but just by translating it in your mind you understand what it means.
Example: "Dark Horse" - One who was previously unknown and is now prominent. In Russian it is pretty much the same thing "Черная Лошадка" or if to translate it to English "Dark Horsey" ("horse" is used with affectionate diminutive suffix).
Source: Russian.