Honestly, I'd say just experiment, and try and look for the patterns in how the monsters show up - many of the monsters have specific behaviors and spawn in certain ways. It's not 100% guaranteed, but it means that if you see a certain pattern on the board, you can guess if there's a decent chance a certain monster will be nearby. I've figured out patterns for the following monsters:
egg, gargoyle, beholder, minotaur, purple slime, slime wizard, romeo & juliet, mine king, gnome
All of the above monsters show up in specific ways, if you can discover how. Once you learn their patterns, you can make educated decisions about what the monsters do and what squares they're likely to be in!
(if anyone else figures out any patterns for rats, bats, skeletons, green slimes, or gladiator ,let me know - these ones still seem random to me)