How do you recommend I learn the cases? They all seem so difficult.
I would recommend a lot of practice in using them in their varied uses. I haven't studied Ukrainian, but I have (sort of) studied other case based languages, E.g. Polish, Old English, Latin; with some of them you can just memorize a few declensions, but Slavic languages are tricky with their hard and soft stems. The way I see it, you could just memorize the hard and soft endings (and whatever else there is) as separate sets or declensions, or just practice with the individual endings, and eventually they'll come to you.