Does anyone have a handy way of remembering declensions?
...Like a chart? I'm having a hard time memorizing the different endings for the cases.
Here's a trick I used to memorize the cases back in college. I made three stacks of cards; one with random nouns, the second with adjectives and the third stack with prepositions (use this page to help - https://en.wikibooks.org/wiki/Russian/Prepositions).
Shuffle the three stacks of cards so that you choose each card at random. Let's say that the first three cards are белый (white), машина (car) and под + instrumental (beneath). Use a declension table (found at http://www.russianlessons.net/) to decline the adjective and noun. So now we have под белой машиной (beneath the white car). You can check your declensions by looking them up on Wiktionary (https://www.wiktionary.org/). After doing this repeatedly with lots of words, eventually you won't need to use declension tables to learn the endings. You can also try different variations of this exercise by including pronouns and verbs. Also realize that the sentences don't have make any sense because you are focusing on learning the declensions.
Wikipedia has declension tables: https://en.wikipedia.org/wiki/Russian_declension#Nouns
However, this might be a little too advanced for beginners.
Tell me about it. I took a year and a half of Russian at my university and spent two months in Russia and I still can't get my cases straight. I have a whiteboard that I would draw out my own tables on when I was studying for exams. I usually just use the russianlessons.net website to look things up quickly, but it's nice to have a real textbook because the tables and explanations of the endings are a little clearer than anything on the internet. I do also have declension table pdfs for each case if you or anyone else wants them.
The best thing our teacher made us do is to learn by heart sample sentences for each case with noun+adj. For example for the dative case "how old is the american president?" (masculin), "how old is the english queen?" (feminine), etc. Charts are way too abstract for me to retain unless I review them often which defeats the object.