When hovering over an ability, the tooltip will tell you whether or not that attack is weak or strong against certain pet types. Additionally, you can hover over the opposing team's pets and view their attacks during combat. This will be important since it’s a good idea to pit a pet that's strong against the opponent's pet who's vulnerable to that type.
Combat is turn-based and there is no time limit on each round in a PVE Pet Battle. You can take your time to determine which spell to use next. Some pet abilities have multiple round cooldowns, while others can do extra damage if certain conditions are met. Be creative and have fun testing which combination of attacks works best against different wild pets!
An advice for those who are trying to compete monopolizers: you cannot beat them by selling for less if they follow right steps. You should do opposite: sell for more. Because market will come down if the price goes unreasonably high. You can set a bid on item for the price it should cost and buy out price for higher than a monopolizer is selling. So, common buyer may get an item for the right price or monopolizer has to buy the item at his loss.