help a college student out with a much needed crash course in kosher!

hi! so for preface, I am not Jewish and my family doesn’t keep a kosher household. So with that being said my grandma is an orthodox Jew and I will be living with her while at college and I have no idea how to keep a Kosher house. I’ve been to her house for some of the big Jewish holidays but past that I really don’t know what’s Kosher aside from that she has special sponges and one is for meat and one is for dairy as i have had helped her with dishes. Aside from that though, what do I need to look for when grocery shopping and are their any food rules aside from no pork, no meat that isn’t blessed by a rabbi, and no mixing meat and dairy that I’m missing? thanks!