What do you mean, "strategy"? Welcome to level three.
A level three trainer will gain an understanding of types, their advantages, and their disadvantages. This essentially allows the trainer to create better and balanced teams. When the trainer has mastered level three, they may try to challenge themselves by performing a monotype run. This is where a trainer will play through a game using only Pokémon that share one type.
The phrase "It's super-effective!" is an addictive notion. Trainers will often use moves with type advantage, even if they actually do less damage than another viable attack. There are eighteen Pokémon types. All Pokémon can be either one or two types. Pokémon with two types are called "dual-types." All types match up in ways that make logical sense in the real world. For example, the Fire-type is super-effective against the Grass-type. Obviously, plants burn easily, so they are weak against fire.
Types match up defensively, too. When one type resists another type's attack, the attack is "not very effective." In this scenario, we call the defending type "strong against" the attacking type. For example, if a Grass-type is attacked by a Water-type, the Grass-type sustains "not very effective" damage since watering a plant is the opposite of strategic.
Some types also have immunities, such as Ground and Flying. Ground is immune to Electric, and Flying takes no damage from Ground. Now for the numbers: when an attack is super-effective, it does double the amount of damage that it would have done. So, if a Water attack with fifty power strikes a Fire-type, then the power is elevated to one hundred, but if that same Water attack strikes a Grass-type, the damage decreases to a mere twenty-five. Dual-type Pokémon are what makes this system a little more complex. If a Pokémon is both a Grass type and a Water-type, then the trainer may attempt a Fire attack. Sure, if the Pokémon was pure Grass, then it would be super effective, but Water resists the attack, so the damage would be neutral. Other Pokémon are both Fire and Rock-type. Rock-types are weak to both Water and Grass-types, so a Grass-type attack would do super-effective damage to the Rock, but not very effective damage to the Fire, so it would be neutral. However, if a Water attack were to strike this Pokémon, then the damage would be super-effective against both the Rock and the Fire, making the damage four times more powerful than normal. Let us refer back to our fifty power Water attack, it would have two hundred power against this particular Pokémon.
There also exists a factor called Same-Type-Attack-Bonus, or STAB. STAB is the effect that occurs when a Pokémon of a certain type uses an attack of that same type. The effect being that the attack gets a fifty percent boost in power. Once again, let us plug in our generic, fifty-power, Water attack. If a Water Pokémon uses this on a Pokémon that takes neutral damage from Water, then the power would be seventy-five. So, if a Water Pokémon uses this Water attack on the Fire and Rock-type, then the power will be a devastating three hundred. Pokémon can often learn many types of moves. It's best to teach a Pokémon moves that vary in types in order to provide coverage against many other types of Pokémon.
For a full and thorough type matchup chart, visit this site: http://bulbapedia.bulbagarden.net/wiki/Type_chart