The Basics
Gameplay
There are two phases of the game. The first phase is the shop phase, where you use a limited supply of 
Gold to buy Pets and Food to improve your team. After that comes the battle phase, where your team goes on to automatically fight other teams people have made.
Shop Phase
At the start of the shop phase, you will have 10 gold which you can spend on Pets, Food and rolling the shop.
At base, all Pets cost three gold to add to your team. Each pet has its own base stats and ability. They have two stats which can be of varying values. 
Attack and 
Health. Attack effects how much health the pet takes away from enemies each time it attacks them and health is how much damage can be lost before the pet faints. Attack and Health are both capped at a max of 50 each. A pets base stats refers to the amount of attack and health they innately have when purchased. The pet's ability will have a varying effect and most will need to have their ability triggered by a certain event in order to be activated with common triggers being Start of battle and End turn. This allows for synergy between certain pets since they benefit off of each others abilities. Buying a copy of a pet that's already on your team and combining them together will result in that pet gaining +1 attack and +1 health in addition to +1 
Experience towards leveling up. All pets are level 1 when first purchased but after a pet gains 2 more experience they will become level 2 and then with an additional 3 experience they will be level 3 - the max level. Levelling up a pet increases the power of their ability by 2 times at level 2 and 3 times at level 3 (relative to their level 1 ability).
Food, like pets, cost three gold each except for the 
Sleeping Pill which only costs one gold. Foods have a large variation in the effects they can give. The most basic effect is for foods to give attack and/or health to a specific pet or multiple random pets. The foods can also grant Food Perks to a specific pet which acts as a sort of equipment that gives extra abilities or large amounts of stats at the cost of each pet only being allowed one food perk at a time. There are other more miscellaneous foods with situational effects such as fainting a pet when it's fed a Sleeping Pill.
Rolling the shop refreshes everything in the shop, giving you new options to choose from barring frozen pets or food. Frozen pets and foods will stay in the left-most slot of the shop until you unfreeze or buy them. Frozen shop items will take up a shop slot and give you less options to choose from. Rolling also occurs at the start of each new shop phase. At the start, you have access to only a couple of available pets and foods. On every odd turn the shop tier will upgrade to a higher tier, gaining access to higher tier pets which have better stats and abilities. You start a game on turn 1 at tier 1, with the shop tier upgrading on turn 3, 5, 7, 9 and 11 where the shop tier remains at 6 until you win or lose. You may gain access to the pets from the next tier earlier by leveling up one of your pets. When a level up occurs you have the option to choose from two pets from the next tier, if it is tier six, you can choose from two tier six pets. This does not happen when two level two pets get combined to level a pet to level 3.
Battle Phase
The battle phase puts your team up against an opposing, user created team of enemy pets. These battles are asynchronous and the game will select an opponent from the database of created teams from the same turn and pit your team up against them.
The first thing that happens during battle is the "Start of battle" which will activate all pets abilities that have that trigger. Then, pets will start automatically attacking each other with your teams right-most pet attacking the opponent's left-most pet at the same time until one (or both) of them are Knocked out. The second right/left most pet will then shuffle forward to face the opposing pet and so on until all pets from at least one team are gone. Keep in mind that pet abilities will heavily impact the overall flow of battle and can lead to some tricky to follow sequences of ability activations - especially at later turns.
If all the opposing pets have fainted and your team still has any number of surviving pets then it is a victory. If all your pets have fainted and the opponent team still has any number of surviving pets then it is a defeat. If both teams have no surviving pets then it is a draw. After battle has concluded you will either gain a Trophy if you won, lose a heart if you lost or gain/lose nothing if it was a draw. No matter the outcome of the previous battle the turn will always increase by one and any Start of turn abilities will trigger unless you were on your last heart and have now lost the game, in which case the run is over.
Modes
There are two main modes you can play in the game. Arena and Versus
Arena
Arena features untimed, asynchronous battles against opponents selected from a pool of teams from players that have a similar playtime to you. The objective is to win 10 battles before losing all your hearts. You start with 5 hearts and will lose 1 every time you lose a battle. You will gain back 1 heart on turn 3 if you had lost at least one battle before then.
Normal Mode
Normal mode is the default way to play the Arena game mode and features the usual 5 hearts (with the option to recover one on turn 3) and no other gameplay differences with Achievements and Snacks being gained through levelling up Pets and completing games.
Easy Mode
Easy mode offers a way for the game to become a large amount easier through the introduction of 2 extra hearts (for a total of 7). The regaining of health on turn 3 is still available and little else changes in terms of gameplay. The caveat to this is that Achievements and Snacks are not available to be earned through playing this difficulty.
This mode is largely used to test less viable Pet compositions that need the extra health to last until the later rounds and is mostly just a way of playing the game in a more unconventional way without being punished as hard.
Hard Mode
Hard mode is a brutal test of skill and resolve that is catered towards experienced players that may find Normal mode to be too easy. It functions the same as Normal mode in that you need to get 10 wins before losing 5 hearts (with the regaining a heart on turn 3 still being available). What makes Hard mode actually hard are the Hard Mode Toys that function similarly to the Toys available in the 
Puppy Pack but instead provide negative effects such as nerfing your teams stats or giving Food Perks to the enemy team. These Hard Mode Toys are forced on the player on every odd turn (excluding turn 1) and you have the option to pick between 2 of them each time, with new Toys only becoming available on later turns.
Versus
Packs
Super Auto Pets houses a variety of Packs - groups of pets and foods crafted to create different and engaging gameplay between them. These packs with preset lineups of Pets are colloquially referred to as "Static Packs" due to their unchanging and predictable nature. There are currently 5 Static Packs in the game:
Turtle Pack (free)
Unicorn Pack ($10.00 USD)
Golden Pack ($10.00 USD)
Star Pack ($10.00 USD)- Puppy Pack ($5.00 USD)
In contrast to these packs are the 
Weekly Pack and 
Custom Packs of which the Weekly pack features random, user curated and content creator packs that cycle every week. Custom Packs allow players to create their own packs using all unlocked pets and foods.
Static Pack players will go against other teams using the same pack unless the "Play against all packs" option is turned on. Custom Pack and Weekly Pack players can only play against other players using the same pack as them.