Monster taming is pretty much having a pet. To tame a pet you need to get something called a taming item. Maybe you can find one at Alberta at the southwest of your map. For example: Rainbow Carrot is for a Lunatic, Unripe Apple is for Porings, and Bitter Herb is for Poporings etc. To see what taming item is for what monster just click on the item and read the description.
From StrategyWiki, the video game walkthrough and strategy guide wiki