The beauty is that these prefixes, being universal, can be added to just about any word adding a flavor you may not have even experienced. Using the same prefixes before a vulgar word makes Russian, perhaps, the most versatile language for cursing.
English uses prepositions instead to modify meaning, as you described.
приехал literal "drove in" переехал "drove over" подъехал "drove up"
> can be added to just about any word adding a flavor you may not have even experienced
That's definitely true. this makes translating from russian lose quite a lot of color.
Flashcards would probably be the fastest method, but I'm not cramming, so to pick up the rest of the characters, I:
- watched the relevant episodes of Спокойной ночи, малыши for letterforms and pronunciation. (phonic segment is about midway through, nearly always at the same time, IIRC)
- read plenty. VK memes at first, news headlines for the proper nouns later.
- watched lyric music videos to work on reading speed.
Be warned, though, that it takes a while for an English speaker to recognize the difference between hard consonants and soft consonants. In fact I got the point where I didn't think that I could tell, but was able to successfully guess 10x in a row. I got them right, but it really felt like I had no idea. Very weird experience.