Dealing with words that have too many meanings

I used to get overwhelmed trying to memorize every single definition of a new word at once. I messed up a practice test yesterday because I mixed up two rare meanings of a verb. My big takeaway is to just learn the context of the exact sentence I'm looking at and ignore the rest. Trying to hoard all the meanings at once just breaks my brain, how do you guys handle polysemy without getting bogged down?