I'm a relatively new barista as well!
One of the tips to help me remember the pumps of syrups in hot drinks is saying "short, short, tall, grande, venti" while putting syrup in. "Short short" puts 2 pumps in a short, then doing "short, short, tall" puts 3 in a hot tall, "short, short, tall, grande" puts 4 in a hot grande, and "short, short, tall, grande, venti" puts 5 in a hot venti. The syrups for iced drinks I remember "34, 67" because it is 3 for an iced tall, 4 for an iced grande, six for an iced venti, and 7 for a trenta.
Another thing I do is ask to make my own drinks on my breaks when it isn't busy. I like to try new drinks so I can better describe them to customers, but also so it gives me a chance to make them.
My last study tip is to use this quizlet:
$1 It has flashcards for syrup pumps and shots for both hot and iced drinks, as well as general barista knowledge (i.e. how to make whipped cream, your jobs under certain roles \[which can vary from store to store\], frappucino scoops, etc.)
Good luck in your new job and welcome to the team!!!