I'm already using strategy, though... Welcome to level six.
A level six trainer will train Pokémon with a combination of strategic move-sets, abilities, and held-items. This step requires an in-depth knowledge of move-pools, abilities, and items. It may also require a solid understanding of breeding and egg-moves, as well as knowledge of hidden abilities.
Just let me explain right off the bat: an all-out offensive moveset would hardly ever be considered "strategic" in competitive battling. First off, there are a few categories that the best Pokémon fit into. There are Fast Sweepers: Pokémon that go first and duke out punishment to entire teams. There are Bulky Sweepers, these are Pokémon that might not be so fast, but are more than capable of taking damage and dishing it right back out. There are several kinds of Walls. There are Defensive Walls, Specially Defensive Walls, HP Walls, and Mixed Walls (Pokémon that embody two or all three of these stats.). Walls are used to set hazards and status conditions. There is a subcategory of Walls called Stallers. These Pokémon will immediately lay out something like a Toxic or Will-O-Wisp, which induces a Poison that steadily increases in damage, or causes a Burn respectively. As Toxic's damage doubles every turn, it seems the more logical choice, but all Burns have the added advantage of slicing it's victim's physical Attack stat in half. A Staller, having set a damaging condition on their victim, will proceed to, well, stall until their opponent has fainted. Effective methods of stalling include the use of Protect and restorative moves such as Recover or Roost.
The Pokémon in the last large category are called Set-Up Pokémon, or simply Set-Ups. Some of these Pokémon are Walls, but some are too weak or frail to fit in any other category. A Set-Up's purpose is to create an environment in which the follow-up Pokémon can completely sweep. This is often done with the use of the move Trick Room, which reverses turn order, causing slower Pokémon to move first. Other times this Pokémon will lay out a weather condition, one of Rain, Sun, Sandstorm, or Hail. Some Set-Ups utilize the move Baton Pass. This move allows the user to switch to another Pokémon and give that Pokémon all of the stat changes that were induced on the user. The greatest example of this is a Pokémon called Ninjask, one of the fastest Pokémon in the game. Ninjask has the Ability Speed Boost, which raises its Speed by one stage every turn. They can also have the move Swords Dance, which raises its Attack by two stages. If a Ninjask, on its first turn, uses Swords Dance, then, by the end of the turn, assuming it hasn't fainted, will have its Speed raised once and its Attack raised twice. Baton Pass those improvements onto a Fast Sweeper, and it will be close to unstoppable.
Now, allow me to elaborate on these "stages" I've just mentioned. Every stat, including two that I have yet to mention, Evasion and Accuracy, can be raised and decreased a maximum of six stages in battle. For Example, If a Pokémon uses the move Swords Dance, then their Attack will be raised two stages. This means that they can only use this move three times before their Attack stat will not go any higher. On the other hand, if a Pokémon is hit with the move Screech, then their Defense will be lowered by two stages. This means that, by the time the Pokémon has sustained three Screeches, its Defense will be as low as it can go. "But how much higher? And how much lower?" You may ask. Well, when raising a stat, every stage counts for +0.33. So, at base, a Pokémon's Attack stat is however much multiplied by 1.0. When it is raised by one stage, that number becomes multiplied by 1.33. Raise it again and that number becomes multiplied by 1.33, and so on and so forth until it piques and is multiplied by more than 5. Now, when a Pokémon's stats are decreasing, it goes from 1.0 to 2/3 to 1/2 to 2/5 to 1/3 to 2/7 reaching its minimum at 1/4. So, the moves Swords Dance and Nasty Plot (which raises the users Special Attack by two stages) are excellent choices on any Sweeper's moveset. Another excellent choice is the move Dragon Dance. This move may only raise the user's Attack by one stage, but it also raises the user's Speed by one stage.
Allow me to talk about those other two stats, Evasion and Accuracy. These two stats are not the stats of a Pokémon, but the stats of its moves. Every move has a power level and an accuracy level. The accuracy level is that move's percent chance of landing. If a move has eighty-five accuracy, then it will hit the opponent eighty-five percent of the time. For those who don't like percentages, that's seventeen times out of twenty. The Accuracy and Evasion stats do not have Evolutionary Values, and they can only be raised or lowered by in-battle stat modifiers. There are some moves that can be used to raise it's users Accuracy, and some moves that lower the target's. The most infamous moves are the ones that raise the user's Evasiveness. Move such as Minimize and Double Team are tournament banned seeing as, with maximized evasiveness, the opponent can only hit its target one fourth of the time at best. Using these moves will earn their user the shameful title of "Evasion Noob." SPme moves, however, have an accuracy of "-." This means that, unless the move doesn't effect the target because of type, the move will always be successful.
Now let's delve into the intricacies of abilities. Every Pokémon has it's own ability, and most Pokémon have two or three possibilities. Knowing which of these abilities better compliments the Pokémon is the key to training your Pokémon correctly. Going over the pros and cons of every ability for every Pokémon would turn this chapter into the size of an encyclopedia. So, instead, I'll simply go over some of the abilities that I think are the best.
The Pokémon Tyranitar has two possible abilities. One is Sand Stream, and the other one is Unnerve. Unnerve makes it so your opponent cannot consume Berries. Strategically, this is usable, but when compared to Sand Stream, it's awful. Sand Stream conjures a Sandstorm upon entering the battlefield. Not only does this increase Rock-types' special defense and damage all non-Rock, Ground, or Steel types, but it also activates several other abilities such as Sand Force and Sand Rush.
Another fantastic ability is Speed Boost. I've already explained this ability, but it is one of the greatest offensive abilities in the game.
Moxie is one the best abilities a Sweeper can have, It makes it so that, when the Pokémon with Moxie defeats an opponent, its Attack stat is raised by one stage. If a Pokémon with Moxie begins a killing streak, it's most likely already over.
Finally, let's talk about held-items. Pokémon have been able to hold items since the second generation games. Back then, the only things they could hold were one of ten types of berries, as well as some Type-Enhancers. These berries could be immediately used by the holding Pokémon when the need arose. When the Pokémon's HP falls below half, it could use a Golden Berry to immediately recover thirty HP. Another example is when a Pokémon is given a Burnt Berry. If this Pokémon is frozen, then they will somehow manage to eat their Berry and thaw themselves out. Today, there are dozens of kinds of Berries, and hundreds of other held items. There are several categories of items. Listed here are only items that have in-battle effects, and all of these items are those that every Pokémon can use.
1) Berries: Berries can do almost anything, from healing off status ailments to increasing a random stat when in peril.
2) Type-Enhancers: These are items that increase the holder's moves of one type by twenty percent.
3) Gems: A different kind of type enhancer. They are consumed after one use, but they make the first successful attack of a certain type land for a thirty percent power increase (fifty percent in Black, White, Black 2 and White 2).
4) Stat Enhancers: These items will increase one stat of the holder. Some of these, called Choice Items, allow for the use of only one move.
5) Incense: These are sort of miscellaneous in battle. One lowers the holder's Speed, another increases the power of the Holder's water attacks, and another one lower's the opponent's Accuracy.
6) Reward Enhancers: These items will take effect even if their holder is only in the battle for one turn. When the opponent is defeated, these items increase some kind of yield. The Lucky Egg increases Experience Point yield by fifty percent. The Amulet Coin doubles the amount of reward money you receive, and the Macho Brace Doubles EV Yields.
Reward Enhancers are irrelevant in tournaments. The way to train a perfect Pokémon is to flawlessly match up moves, abilities and held-items.
It's worth mentioning that some Pokémon can only get certain moves through breeding. These are called egg-moves. Several Pokémon have similar body shapes to others, and this allows them to breed with each other. Breeding is performed well off-screen in the Pokémon Day Care. In order to breed for egg moves, the trainer must have a female of the species they want, and a male with the moves they want. Leave these Pokémon in the Day Care, and they will do the rest. Simply remember that most moves simply can't be learned, and one should look up which moves can be attained by breeding before mixing and matching.
Another thing worth mentioning is that almost every Pokémon has a hidden ability. These are abilities that can only be obtained the Dream World in Black and White, or the Friend Safari in X and Y, these abilities are often much better than the normal ones, and worth the extra effort.