What is a 'perfect IV Pokemon' and how do I get one?

First of all, you need to know the meaning of IV and EV.

• IV (stands for Individual Values) are the Pokémon equivalent of genes. They are instrumental in determining the stats of a Pokémon, being responsible for the large variation in stats among untrained Pokémon of the same species. IVs range from 0-31.

• EV (stands for Effort Values) are attributes which give bonuses to an individual Pokémon's stats and improve differently depending which Pokémon they defeat. Each Pokemon species gives a specific amount of EVs.
  Here's the complete list of EVs yield by each Pokemon.

How do IVs work?

IVs are determined when you first encounter a Pokemon, when you hatch it or when you obtain it. The only way to influence IVs is Pokemon breeding because the offspring will inherit some IVs from their parents.

A perfect IV Pokemon is a Pokemon with some its IVs (usually 4-5 of them) at the maximum value of 31. This can be extended to the right Nature, too.

To see your Pokemon's IVs you need an NPC called the IV Judge (or Stats Judge), which is located at the Battle Tree. Rather than judging Pokémon himself, however, he instead gives the player an upgrade to their PC to judge Pokémon, but only after the player has hatched at least 21 Pokémon Eggs.

Here's how to understand the IV judge statements:

IV Specific:
IV of 0: "No Good"
IV range of 1-15: "Decent"
IV range of 16-25: "Pretty Good"
IV range 26-29: "Very Good"
IV of 30: "Fantastic"
IV of 31: "Best"

IV Total:
151 to 186 | Outstanding potential!
121 to 150 | Relatively superior potential
91 to 120 | Above-average potential
0 to 90 | Decent potential

How do EVs work?

In Generation VII, Pokémon are limited to a total of 252 EVs per stat, and 510 EVs in total. As a result, the maximum amount of additional stat points that can be acquired by EV-training for a given stat is 63, in comparison to a Pokémon that is uninvested in EVs.

Just for reference, this is how a stat is calculated:

Pressing the Y button on a Pokémon's Summary screen will show a graph depicting the EVs it has accumulated so far; stats that have reached 252 effort values will sparkle.

How to give EVs to a Pokemon?

There are different methods:

• Power Items are a series of items which give an additional 8 EVs per Pokémon defeated. Each applies the bonus to a different stat, in addition to the normal EVs gained.

• Pokerus, a rare status condition which doubles the effort points gained in battle. More info about Pokerus here.

• SOS Battles, is when a wild Pokémon can call an ally for help, turning a regular wild battle into an SOS Battle. All wild Pokémon summoned this way have their EV yields doubled upon being defeated.

• Poké Pelago, which allows for passive EV-training of Pokémon currently stored in the PC. On Isle Evelup, these Pokémon can be let out to play on one of three structures on the isle. Each round lasts for 30 minutes. During play sessions, special juices are given to the Pokémon, allowing for increases in EVs per stat. The effectiveness of these juices is determined by Isle Evelup's level.
  Since the maximum EVs a Pokémon can get in any one stat is 252, it would take 63 sessions at Level 3 to max out one stat, for a total time of 31 hours and 30 minutes.

• Festival Plaza's attractions, Bouncy Houses and Food Stalls, can alter a Pokémon's EVs for a predetermined price.

Example:

If a Pokémon holding a Power Weight and infected with Pokérus defeats a Caterpie, which gives 1 HP EV, it will earn 18 HP EVs

(1 from Caterpie + 8 for Power Item) x 2 from Pokerus = 18 EVs

However, a Caterpie that is called as an ally will instead yield 36 HP EVs

(1 from Caterpie + 8 for Power Item) x 2 from Pokerus x 2 SOS battle bonus = 36 EVs

In this way, only 7 ally Caterpie must be defeated to max out HP.