I know it explained in the tutorial but I forgot and I can't seem to figure out how to get vermillion. If someone could help me on this I would be very grateful. (I've only been a Beast Keeper for 3 days now.)

Vermillion can be found in Explore, just lying around in piles of 1-3 units. You can also buy it if anyone is selling it. Occasionally pets from Quests will also bring back vermillion. Lastly if you have enough you can build a Golem which will automatically create more vermillion for you.

There is also the battlefield but I would not advise you to go there right now.

Thanks. I actually found some Vermillion shortly after I made this post, lol. Stuff like that happens to me all the time, so I'm not really surprised. I didn't know about the golems though. How do you get the scheme/recipe things for those? I can't find any in the shops.

Lots of people sell golem schemes since they can only be used once. You can find them pretty cheap in Item Trades, or randomly pick them up in Explore from one of the buildings or a treasure chest behind a Guardian monster.

Once you've got enough vermillion, the golem will basically take it and double it. 

If you want to get lots of vermillion quickly, buy yourself a fairly decent pet from the pet trades (look for firebreath dragons, acid spit cockatrices, lightning rocs, and ice breath lykoses) and go to the Volcano biotope. Fight some Lava Crystal guardians, and they will give you on average 7 vermillion each.