Using the LivingThings Lexicon and Crafting Basics
Get the Lexicon First
Craft the LivingThings Lexicon before you go hunting. It is the in-game reference for the mod's creatures and items, so keep it in your hotbar and open it whenever you meet something unfamiliar. The mod's only crafting_shapeless recipe is the one you use here, so check the lexicon entry for the exact arrangement rather than guessing a shaped grid.
Read Entries Before You Explore
Open the LivingThings Lexicon and read the entry for each creature you plan to find. Entries cover the spawn eggs you will need, such as Ancient Blaze Spawn Egg, Baby Enderdragon Spawn Egg, Crab Spawn Egg, Elephant Spawn Egg, Flamingo Spawn Egg, Giraffe Spawn Egg, Koala Spawn Egg, Lion Spawn Egg, Mantaray Spawn Egg, Monkey Spawn Egg, Nether Knight Spawn Egg, Ostrich Spawn Egg, Owl Spawn Egg, Peacock Spawn Egg, Penguin Spawn Egg, Raccoon Spawn Egg, Seahorse Spawn Egg, Shark Spawn Egg, Shroomie Spawn Egg, and Snail Spawn Egg.
Gather Materials
Some creatures drop materials you will want to store: Crab Shell from crabs, Shark Tooth from sharks, and Banana as a plant item. Seahorse Bucket holds a captured seahorse. Keep these in labeled chests so you can find them when a lexicon entry calls for them.
Workflow
1. Craft the LivingThings Lexicon.
2. Read the entry for your target creature.
3. Spawn or locate it, then collect its drops.
4. Return to the lexicon to see what the drop is used for.
Repeat this loop for each new creature instead of experimenting blindly.