Here's a quick guide for anyone new to this sort of pokemon battling, feel free to ask if you have any questions!
Pokemon Online is a battle simulator that precisely replicates the battle system used in Nintendo's series of Pokemon games. You are able to choose and customise your Pokémon team with full control over the options and mechanics present in the games and battle instantly with other players through your web browser or the downloadable app versions on Mac and PC.
For several years Pokemon Online and the battling community Smogon have partnered to provide the most popular source of Pokémon battling outside of the 3DS games themselves.
Smogon is the largest community of competitive Pokemon battling, and their formats or "metagames" have become the most commonly accepted sets of rules for playing Pokemon battles by. These rulesets are intended to provide the fair and balanced playing fields that minimise the influence of luck and try to keep the focus on the players' team composition and skill.
OverUsed, more commonly abbreviated to OU, is widely regarded as the "standard" format for Pokémon battling. It is characterised by primarily restricting access to the the most overpowered elements of the game that would otherwise dominate and unbalance the wider metagame. This essentially boils down to a concise banlist which can be found here- if it's on that list, it's off limits, if it's not there, you can use it on your teams.
For the most part if you've played a recent Pokémon game you'll probably be familiar with almost all aspects of the Pokémon Online teambuilder when it comes to choosing the attributes of each pokemon- species, moves, abilities, items, and so on. However there are two attributes that go largely unmentioned in the core game series and are never full explained, and those are EVs (effort values) and IVs (individual values). However both have a significant effect on the stats of your Pokémon and for a pokemon tournament, knowing how they work is very helpful!
*EVs are most commonly gained through battling other pokemon, with each species awarding a Pokémon EV points for a particular stat when it makes them faint (for example Pikachu gives the victorious Pokémon two speed EVs). For every 4 EVs gained in a stat, that stat is raised by 1 point. A Pokémon can gain up to 510 EVs total, with a maximum of 255 EVs in a single stat (however because EVs are only useful in multiples of 4, the maximum effective EVs per stat is 252).
So a quick bit of maths shows us that if you gain 252 EV points in one stat, that stat will be 64 points higher than if it had none. This is obviously a massive increase, and shows the importance of good allocation of EVs. For example if you have an aggressive but frail Pokémon like Talonflame, EVs are best invested into its attack and speed stats, since its poor defences will not benefit from them very much while being of no use at all in SpAtt if no special attacking moves are chosen.
*IVs also influence stats, but rather than being gained each pokemon has them randomly decided at the moment it is obtained (or, if bred from an egg, from the moment the egg is laid). A pokemon has between 0 and 31 IVs in each stat, with each IV representing one stat point, so a Pokémon with 30 attack IVs will have 5 more attack points than a pokemon with 25 IVs that's raised in the exact same way.
For the most part Pokémon Online makes this simple by defaulting all IVs to their maximum of 31 for the highest possible stat line, however there are a few instances where it is beneficial to lower one or more values. For example Pokémon that do not use physical attacks may choose to minimise their attack IVs to minimise the damage they take if they suffer from the Confuse condition, or speed may be reduced to make the Pokémon as slow as possible for using moves where going last is beneficial, or if the player chooses to use Trick Room to make the slowest pokemon attack first instead.
The other main reason to change IVs is that they are responsible for determining the type and power level of the move Hidden Power. The formula for this move is rather complicated, but if you do want to use Hidden Power on one of your Pokémon you just need to choose the version with the desired type on the move selection part of the teambuilder and Pokémon Online will adjust their IVs automatically.
*While the general idea of natures is explained, that they increase the maximum value of one stat and decrease another (there are also neutral natures that change no stats), the exact amount is not mentioned in the games. That amount is 10%, so quite a good chunk! As a general rule it is best to choose a nature that does increase and decrease a stat, as almost every moveset of a pokemon will benefit while having one unused stat that can afford to be lowered.
If this is your first taste of multiplayer battling, or just want to get more competitive to improve your chances of winning the tournament, be sure to spend some time on smogon.com. They have tons of articles and guides, as well as a "strategy pokedex" with examples of the most effective sets for each Pokémon. It's a great source of information and should give you some information to start building your teams!