Personally the method I'm finding easiest is to narrow down what series it could be, check the decks that match the colour and then compare the names listed in the hints and the deck data.

A lot of them you can actually pick out the clothing in the card image, and even if you can't the hints given tend to match something in the description or deck name. You just need to do a bit of googling and digging around, I'm sure you'll do fine!