Well, I'll explain the little I know.
Each climate produces a certain function, for example: Ninetales has the Drought ability, which summons the sun, other Pokemon need the sun to unleash their abilities, eg Venusaur has the ability Chlorophyll, which doubles the speed while the sun is shining strong, another skill which needs the sun is the Solar Power that makes the Pokemon lose 12.5% HP, but the special attack increases by 50%.
The Rain is summoned by skill, skill used by Politoed and Pelipper, and again other Pokemon will need rain, such as: Kindra with Swifth Swin, which will double speed during the rain, and Ludicolo's Rain Dish that heals 1/16 of Maximum HP in the rain.
In Sandstorm summoned by the Sand Stream ability the Pokemon that possess these abilities are: Tyranitar, Hippowdon and Gigalith. The skills needed by Sandstorm are: Sand Force, which increases the power of Ground, Rock and Steel attacks by 30% in a sandstorm. Sand Rush, which doubles the speed and Sand Veil, that evasion increases by 20% in a sandstorm.
If you use a Ninetales that has Drought and your opponent shortly after that put a Politoed with Drizze, the climate that will stand out will be the one that has been placed last.