>>45215971Serebii has a good guide on EVs/IVs, natures etc.
I can also give you a brief rundown:
EVs(Effort Values): Hidden stat points that you get from battling Pokémon, there are EVs for every major stat(HP, ATK, DEF, SPATK,SPDEF,SPEED). At level 100, 4 EVs = 1 extra point towards that stat. You can have a maximum of 510 EVs on a Pokémon.
IVs(Individual Values): These are also stats points assigned to each major stat that are hidden. Unlike EVs, IVs are fixed in place onto a Pokemon and cannot be changed. Each Pokémon can have 0-31 IVs. At level 100, each IV = 1 extra point towards its respective stat.
Natures: Natures are very simple, most natures increase a major stat by 10% and decrease another by the same amount. There are also neutral natures that don't increase or decrease any stats.
Abilities: Straightforward, these are additional effects that a Pokémon has on itself and other Pokémon in the battle. Abilities are diverse and can do a variety of things.
Competitive Formats:
Smogon: This is a long running fanmade and managed competitive community. They offer a variety of metagames with the most popular being their 6v6 formats. Smogon breaks the roster of Pokémon into 'tiers' with the most powerful mons at the highest tiers so the least powerful pokemon can shine in the lower tiers. A Pokemon from a higher tier cannot be used in a lower tier, but a Pokemon from a lower tier can be used in higher tiers(since they're relatively weak anyways).
VGC: This is the official competitive format sanctioned by TPCi. The format is double battles with a bring 6 pick 4 format. The mons that can legally be used changes with every 'Series'.
3v3 singles: This is also a format played on cart. The legal Pokemon changes just like VGC with every 'series'.
