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Learning new languages has been scientifically shown to improve the exact thing you are looking for.
Language learning doesn't have to be wrote memorization, although that IS the best method, in terms of skill gained divided by time invested.
An alternative approach is to incorporate your new language in to things you already do.
Enjoy video games? Change the menu/dialogue/subtitle language. Or try duolingo. It's like a game, it works on the same reward mechanisms that keep you hooked on your electronic toys.
Like movies? Watch movies with subtitles that aren't in your native language, comparing them with the audio and the visuals you see. Your brain will do the rest. However, this without suplementary learning will lead to weebitis - you know how weeaboos think they can perfectly speak a language from watching anime? Well, technically they are learning japanese, just very inefficiently.
Like learning/reading in general? Get a dictionary from your library and translate wikipedia articles in the language you are trying to learn about subjects you care for. This specifically is something you can do once you have some knowledge of the language, if you do this off the bat you'll just be confused and in the dark.
